tests/testthat/_snaps/fmt_markdown.md

In rstudio/gt: Easily Create Presentation-Ready Display Tables

LaTeX formulas render correctly in HTML

Code
  gt_tbl$`_boxhead`$column_label
Output
  [[1]]
  [1] "idx"

  [[2]]
  [1] "Time Domain<br/>$\\small{f\\left( t \\right) = {\\mathcal{L}^{\\,\\, - 1}}\\left\\{ {F\\left( s \\right)} \\right\\}}$"
  attr(,"class")
  [1] "from_markdown"

  [[3]]
  [1] "$s$ Domain<br/>$\\small{F\\left( s \\right) = \\mathcal{L}\\left\\{ {f\\left( t \\right)} \\right\\}}$"
  attr(,"class")
  [1] "from_markdown"

Code
  cat(render_as_html(gt_tbl))
Output
  <table class="gt_table" style="table-layout:fixed;width:0px;" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
    <colgroup>
      <col style="width:50px;"/>
      <col style="width:300px;"/>
      <col style="width:600px;"/>
    </colgroup>
    <thead>
      <tr class="gt_heading">
        <td colspan="3" class="gt_heading gt_title gt_font_normal" style><span class='gt_from_md'>A Table of Laplace Transforms — <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathsize="0.9em"><mi mathvariant="script">L</mi></mstyle></mrow><annotation encoding="application/x-tex">\small{{\mathcal{L}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.615em;"></span><span class="mord sizing reset-size6 size5"><span class="mord"><span class="mord mathcal">L</span></span></span></span></span></span></span></td>
      </tr>
      <tr class="gt_heading">
        <td colspan="3" class="gt_heading gt_subtitle gt_font_normal gt_bottom_border" style><span class='gt_from_md'>The most commonly used Laplace transforms and formulas.<br/><br/></span></td>
      </tr>
      <tr class="gt_col_headings">
        <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="a::stub"></th>
        <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="l_time_domain"><span class='gt_from_md'>Time Domain<br/><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathsize="0.9em"><mrow><mi>f</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mo>=</mo><msup><mi mathvariant="script">L</mi><mrow><mtext> </mtext><mtext> </mtext><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo fence="true">{</mo><mrow><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow></mrow><mo fence="true">}</mo></mrow></mrow></mstyle></mrow><annotation encoding="application/x-tex">\small{f\left( t \right) = {\mathcal{L}^{\,\, - 1}}\left\{ {F\left( s \right)} \right\}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.2725em;"></span><span class="mord sizing reset-size6 size5"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen sizing reset-size5 size6 delimcenter" style="top:0.025em;">(</span><span class="mord mathnormal">t</span><span class="mclose sizing reset-size5 size6 delimcenter" style="top:0.025em;">)</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7926em;"><span style="top:-2.963em;margin-right:0.0556em;"><span class="pstrut" style="height:2.6em;"></span><span class="sizing reset-size5 size2 mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.2453em;"></span><span class="mspace mtight" style="margin-right:0.2453em;"></span><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen sizing reset-size5 size6 delimcenter" style="top:0.025em;">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen sizing reset-size5 size6 delimcenter" style="top:0.025em;">(</span><span class="mord mathnormal">s</span><span class="mclose sizing reset-size5 size6 delimcenter" style="top:0.025em;">)</span></span></span><span class="mclose sizing reset-size5 size6 delimcenter" style="top:0.025em;">}</span></span></span></span></span></span></span></th>
        <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="l_laplace_s_domain"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi></mrow><annotation encoding="application/x-tex">s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">s</span></span></span></span> Domain<br/><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathsize="0.9em"><mrow><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow><mo>=</mo><mi mathvariant="script">L</mi><mrow><mo fence="true">{</mo><mrow><mi>f</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mrow><mo fence="true">}</mo></mrow></mrow></mstyle></mrow><annotation encoding="application/x-tex">\small{F\left( s \right) = \mathcal{L}\left\{ {f\left( t \right)} \right\}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.2725em;"></span><span class="mord sizing reset-size6 size5"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen sizing reset-size5 size6 delimcenter" style="top:0.025em;">(</span><span class="mord mathnormal">s</span><span class="mclose sizing reset-size5 size6 delimcenter" style="top:0.025em;">)</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathcal">L</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen sizing reset-size5 size6 delimcenter" style="top:0.025em;">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen sizing reset-size5 size6 delimcenter" style="top:0.025em;">(</span><span class="mord mathnormal">t</span><span class="mclose sizing reset-size5 size6 delimcenter" style="top:0.025em;">)</span></span></span><span class="mclose sizing reset-size5 size6 delimcenter" style="top:0.025em;">}</span></span></span></span></span></span></span></th>
      </tr>
    </thead>
    <tbody class="gt_table_body">
      <tr><th id="stub_1_1" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>1</span></th>
  <td headers="stub_1_1 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></td>
  <td headers="stub_1_1 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>1</mn><mi>s</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">s</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_2" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>2</span></th>
  <td headers="stub_1_2 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mi>a</mi><mtext> </mtext><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{a\,t}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7936em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7936em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span></td>
  <td headers="stub_1_2 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>1</mn><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{{s - a}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_3" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>3</span></th>
  <td headers="stub_1_3 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>t</mi><mi>n</mi></msup><mo separator="true">,</mo><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>n</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">{t^n},\,\,\,\,\,n = 1,2,3, \ldots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8588em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></td>
  <td headers="stub_1_3 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>n</mi><mo stretchy="false">!</mo></mrow><msup><mi>s</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{n!}}{{{s^{n + 1}}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">n</span><span class="mclose">!</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_4" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>4</span></th>
  <td headers="stub_1_4 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>t</mi><mi>p</mi></msup><mo separator="true">,</mo><mi>p</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">{t^p}, p &gt; -1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8588em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">1</span></span></span></span></span></td>
  <td headers="stub_1_4 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi mathvariant="normal">Γ</mi><mrow><mo fence="true">(</mo><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow><mo fence="true">)</mo></mrow></mrow><msup><mi>s</mi><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{\Gamma \left( {p + 1} \right)}}{{{s^{p + 1}}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">p</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord">Γ</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_5" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>5</span></th>
  <td headers="stub_1_5 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mi>t</mi></msqrt></mrow><annotation encoding="application/x-tex">\sqrt t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.1475em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8925em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="padding-left:0.833em;">t</span></span><span style="top:-2.8525em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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  <td headers="stub_1_5 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><msqrt><mi>π</mi></msqrt><mrow><mn>2</mn><msup><mi>s</mi><mfrac><mn>3</mn><mn>2</mn></mfrac></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{{\sqrt \pi }}{{2{s^{\frac{3}{2}}}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.3068em;vertical-align:-0.8296em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4773em;"><span style="top:-2.1704em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord">2</span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9396em;"><span style="top:-3.3486em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8003em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;padding-left:0.833em;">π</span></span><span style="top:-2.7603em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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      <tr><th id="stub_1_6" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>6</span></th>
  <td headers="stub_1_6 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>t</mi><mrow><mi>n</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup><mo separator="true">,</mo><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>n</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">{t^{n - \frac{1}{2}}},\,\,\,\,\,n = 1,2,3, \ldots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1485em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></td>
  <td headers="stub_1_6 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mn>1</mn><mo>⋅</mo><mn>3</mn><mo>⋅</mo><mn>5</mn><mo>⋯</mo><mrow><mo fence="true">(</mo><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo fence="true">)</mo></mrow><msqrt><mi>π</mi></msqrt></mrow><mrow><msup><mn>2</mn><mi>n</mi></msup><msup><mi>s</mi><mrow><mi>n</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{{1 \cdot 3 \cdot 5 \cdots \left( {2n - 1} \right)\sqrt \pi }}{{{2^n}{s^{n + \frac{1}{2}}}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.3069em;vertical-align:-0.8296em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4773em;"><span style="top:-2.1704em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.5904em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9396em;"><span style="top:-3.3486em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord">2</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8003em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;padding-left:0.833em;">π</span></span><span style="top:-2.7603em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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      <tr><th id="stub_1_7" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>7</span></th>
  <td headers="stub_1_7 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\sin \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_7 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mi>a</mi><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{a}{{{s^2} + {a^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8769em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_8" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>8</span></th>
  <td headers="stub_1_8 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\cos \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_8 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mi>s</mi><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{s}{{{s^2} + {a^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8769em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_9" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>9</span></th>
  <td headers="stub_1_9 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">t\sin \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_9 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mn>2</mn><mi>a</mi><mi>s</mi></mrow><msup><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{2as}}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4154em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord">2</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_10" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>10</span></th>
  <td headers="stub_1_10 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">t\cos \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_10 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>−</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><msup><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{{s^2} - {a^2}}}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.5851em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_11" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>11</span></th>
  <td headers="stub_1_11 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow><mo>−</mo><mi>a</mi><mi>t</mi><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\sin \left( {at} \right) - at\cos \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_11 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mn>2</mn><msup><mi>a</mi><mn>3</mn></msup></mrow><msup><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{2{a^3}}}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.5851em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord">2</span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_12" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>12</span></th>
  <td headers="stub_1_12 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow><mo>+</mo><mi>a</mi><mi>t</mi><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\sin \left( {at} \right) + at\cos \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_12 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mn>2</mn><mi>a</mi><msup><mi>s</mi><mn>2</mn></msup></mrow><msup><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{2a{s^2}}}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.5851em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord">2</span><span class="mord mathnormal">a</span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_13" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>13</span></th>
  <td headers="stub_1_13 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow><mo>−</mo><mi>a</mi><mi>t</mi><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\cos \left( {at} \right) - at\sin \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_13 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>s</mi><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>−</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow></mrow><msup><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{s\left( {{s^2} - {a^2}} \right)}}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.684em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_14" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>14</span></th>
  <td headers="stub_1_14 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow><mo>+</mo><mi>a</mi><mi>t</mi><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\cos \left( {at} \right) + at\sin \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_14 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>s</mi><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow></mrow><msup><mrow><mo fence="true">(</mo><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{s\left( {{s^2} + 3{a^2}} \right)}}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.684em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.74em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_15" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>15</span></th>
  <td headers="stub_1_15 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi><mo>+</mo><mi>b</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\sin \left( {at + b} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">b</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_15 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>s</mi><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mi>b</mi><mo fence="true">)</mo></mrow><mo>+</mo><mi>a</mi><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mi>b</mi><mo fence="true">)</mo></mrow></mrow><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{{s\sin \left( b \right) + a\cos \left( b \right)}}{{{s^2} + {a^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.1963em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">b</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">b</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_16" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>16</span></th>
  <td headers="stub_1_16 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi><mo>+</mo><mi>b</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\cos \left( {at + b} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">b</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_16 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>s</mi><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mi>b</mi><mo fence="true">)</mo></mrow><mo>−</mo><mi>a</mi><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mi>b</mi><mo fence="true">)</mo></mrow></mrow><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{{s\cos \left( b \right) - a\sin \left( b \right)}}{{{s^2} + {a^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.1963em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">b</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">b</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_17" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>17</span></th>
  <td headers="stub_1_17 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sinh</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\sinh \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">sinh</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_17 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mi>a</mi><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>−</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{a}{{{s^2} - {a^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8769em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_18" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>18</span></th>
  <td headers="stub_1_18 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>cosh</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>a</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\cosh \left( {at} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cosh</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_18 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mi>s</mi><mrow><msup><mi>s</mi><mn>2</mn></msup><mo>−</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{s}{{{s^2} - {a^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8769em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_19" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>19</span></th>
  <td headers="stub_1_19 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mi>a</mi><mi>t</mi></mrow></msup><mi>sin</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>b</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{at}}\sin \left( {bt} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0436em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7936em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">b</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_19 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mi>b</mi><mrow><msup><mrow><mo fence="true">(</mo><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{b}{{{{\left( {s - a} \right)}^2} + {b^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4654em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_20" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>20</span></th>
  <td headers="stub_1_20 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mi>a</mi><mi>t</mi></mrow></msup><mi>cos</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>b</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{at}}\cos \left( {bt} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0436em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7936em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">b</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_20 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow><mrow><msup><mrow><mo fence="true">(</mo><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{{s - a}}{{{{\left( {s - a} \right)}^2} + {b^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.3543em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_21" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>21</span></th>
  <td headers="stub_1_21 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mi>a</mi><mi>t</mi></mrow></msup><mi>sinh</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>b</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{at}}\sinh \left( {bt} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0436em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7936em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sinh</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">b</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_21 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mi>b</mi><mrow><msup><mrow><mo fence="true">(</mo><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>−</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{b}{{{{\left( {s - a} \right)}^2} - {b^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4654em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_22" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>22</span></th>
  <td headers="stub_1_22 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mi>a</mi><mi>t</mi></mrow></msup><mi>cosh</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mrow><mi>b</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{at}}\cosh \left( {bt} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0436em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7936em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cosh</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">b</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_22 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow><mrow><msup><mrow><mo fence="true">(</mo><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>−</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{{s - a}}{{{{\left( {s - a} \right)}^2} - {b^2}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.3543em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_23" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>23</span></th>
  <td headers="stub_1_23 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>t</mi><mi>n</mi></msup><msup><mi mathvariant="bold">e</mi><mrow><mi>a</mi><mi>t</mi></mrow></msup><mo separator="true">,</mo><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>n</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">{t^n}{{\bf{e}}^{at}},\,\,\,\,\,n = 1,2,3, \ldots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.988em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7936em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></td>
  <td headers="stub_1_23 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>n</mi><mo stretchy="false">!</mo></mrow><msup><mrow><mo fence="true">(</mo><mrow><mi>s</mi><mo>−</mo><mi>a</mi></mrow><mo fence="true">)</mo></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{{n!}}{{{{\left( {s - a} \right)}^{n + 1}}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4654em;vertical-align:-1.094em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.156em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">n</span><span class="mclose">!</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.094em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_24" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>24</span></th>
  <td headers="stub_1_24 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo fence="true">(</mo><mrow><mi>c</mi><mi>t</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f\left( {ct} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">c</span><span class="mord mathnormal">t</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_24 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>1</mn><mi>c</mi></mfrac><mi>F</mi><mrow><mo fence="true">(</mo><mfrac><mi>s</mi><mi>c</mi></mfrac><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\frac{1}{c}F\left( {\frac{s}{c}} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">c</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">c</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">)</span></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_25" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>25</span></th>
  <td headers="stub_1_25 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>c</mi></msub><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mo>=</mo><mi>u</mi><mrow><mo fence="true">(</mo><mrow><mi>t</mi><mo>−</mo><mi>c</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{u_c}\left( t \right) = u\left( {t - c} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">u</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">c</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span><span style="white-space:nowrap;font-style:normal;font-weight:bold;line-height:0;">[1]</span></td>
  <td headers="stub_1_25 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>c</mi><mi>s</mi></mrow></msup><mi>s</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{{{{\bf{e}}^{ - cs}}}}{s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.1343em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4483em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">s</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7713em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">cs</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_26" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>26</span></th>
  <td headers="stub_1_26 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi><mrow><mo fence="true">(</mo><mrow><mi>t</mi><mo>−</mo><mi>c</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">\delta \left( {t - c} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">c</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span><span style="white-space:nowrap;font-style:normal;font-weight:bold;line-height:0;">[2]</span></td>
  <td headers="stub_1_26 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>c</mi><mi>s</mi></mrow></msup></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{ - cs}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7713em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7713em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">cs</span></span></span></span></span></span></span></span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_27" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>27</span></th>
  <td headers="stub_1_27 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>c</mi></msub><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mi>f</mi><mrow><mo fence="true">(</mo><mrow><mi>t</mi><mo>−</mo><mi>c</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{u_c}\left( t \right)f\left( {t - c} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">c</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_27 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>c</mi><mi>s</mi></mrow></msup><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{ - cs}}F\left( s \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0213em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7713em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">cs</span></span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_28" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>28</span></th>
  <td headers="stub_1_28 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>c</mi></msub><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mi>g</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{u_c}\left( t \right)g\left( t \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_28 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>c</mi><mi>s</mi></mrow></msup><mi mathvariant="script">L</mi><mrow><mo fence="true">{</mo><mrow><mi>g</mi><mrow><mo fence="true">(</mo><mrow><mi>t</mi><mo>+</mo><mi>c</mi></mrow><mo fence="true">)</mo></mrow></mrow><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{ - cs}}{\mathcal{L}}\left\{ {g\left( {t + c} \right)} \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0213em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7713em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">cs</span></span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathcal">L</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">c</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_29" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>29</span></th>
  <td headers="stub_1_29 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">e</mi><mrow><mi>c</mi><mi>t</mi></mrow></msup><mi>f</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{{\bf{e}}^{ct}}f\left( t \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0436em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7936em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_29 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mrow><mo fence="true">(</mo><mrow><mi>s</mi><mo>−</mo><mi>c</mi></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">F\left( {s - c} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">c</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_30" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>30</span></th>
  <td headers="stub_1_30 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>t</mi><mi>n</mi></msup><mi>f</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mo separator="true">,</mo><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi>n</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">{t^n}f\left( t \right),\,\,\,\,\,n = 1,2,3, \ldots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></td>
  <td headers="stub_1_30 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo fence="true">)</mo></mrow><mi>n</mi></msup><msup><mi>F</mi><mrow><mo fence="true">(</mo><mi>n</mi><mo fence="true">)</mo></mrow></msup><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{\left( { - 1} \right)^n}{F^{\left( n \right)}}\left( s \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord">−</span><span class="mord">1</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">(</span></span><span class="mord mathnormal mtight">n</span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">)</span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_31" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>31</span></th>
  <td headers="stub_1_31 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>1</mn><mi>t</mi></mfrac><mi>f</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \frac{1}{t}f\left( t \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">t</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_31 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∫</mo><mrow><mtext> </mtext><mi>s</mi></mrow><mrow><mtext> </mtext><mi mathvariant="normal">∞</mi></mrow></msubsup><mrow><mi>F</mi><mrow><mo fence="true">(</mo><mi>u</mi><mo fence="true">)</mo></mrow><mtext> </mtext><mi>d</mi><mi>u</mi></mrow></mrow><annotation encoding="application/x-tex">\int_{{\,s}}^{{\,\infty }}{{F\left( u \right)\,du}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2151em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight">s</span></span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight">∞</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">u</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">u</span></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_32" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>32</span></th>
  <td headers="stub_1_32 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><msubsup><mo>∫</mo><mrow><mtext> </mtext><mn>0</mn></mrow><mrow><mtext> </mtext><mi>t</mi></mrow></msubsup><mrow><mtext> </mtext><mi>f</mi><mrow><mo fence="true">(</mo><mi>v</mi><mo fence="true">)</mo></mrow><mtext> </mtext><mi>d</mi><mi>v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \int_{{\,0}}^{{\,t}}{{\,f\left( v \right)\,dv}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4554em;vertical-align:-0.9119em;"></span><span class="mop"><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5435em;"><span style="top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight">0</span></span></span></span></span><span style="top:-3.8129em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight">t</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9119em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></td>
  <td headers="stub_1_32 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow></mrow><mi>s</mi></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \frac{{F\left( s \right)}}{s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">s</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_33" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>33</span></th>
  <td headers="stub_1_33 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><msubsup><mo>∫</mo><mrow><mtext> </mtext><mn>0</mn></mrow><mrow><mtext> </mtext><mi>t</mi></mrow></msubsup><mrow><mi>f</mi><mrow><mo fence="true">(</mo><mrow><mi>t</mi><mo>−</mo><mi>τ</mi></mrow><mo fence="true">)</mo></mrow><mi>g</mi><mrow><mo fence="true">(</mo><mi>τ</mi><mo fence="true">)</mo></mrow><mtext> </mtext><mi>d</mi><mi>τ</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \int_{{\,0}}^{{\,t}}{{f\left( {t - \tau } \right)g\left( \tau  \right)\,d\tau }}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4554em;vertical-align:-0.9119em;"></span><span class="mop"><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5435em;"><span style="top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight">0</span></span></span></span></span><span style="top:-3.8129em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight">t</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9119em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span></span></span></span></span></span></span></td>
  <td headers="stub_1_33 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow><mi>G</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">F\left( s \right)G\left( s \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_34" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>34</span></th>
  <td headers="stub_1_34 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo fence="true">(</mo><mrow><mi>t</mi><mo>+</mo><mi>T</mi></mrow><mo fence="true">)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f\left( {t + T} \right) = f\left( t \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span></span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_34 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mstyle scriptlevel="0" displaystyle="true"><msubsup><mo>∫</mo><mrow><mtext> </mtext><mn>0</mn></mrow><mrow><mtext> </mtext><mi>T</mi></mrow></msubsup><mrow><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>s</mi><mi>t</mi></mrow></msup><mi>f</mi><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mtext> </mtext><mi>d</mi><mi>t</mi></mrow></mstyle><mrow><mn>1</mn><mo>−</mo><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>s</mi><mi>T</mi></mrow></msup></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \frac{{\displaystyle \int_{{\,0}}^{{\,T}}{{{{\bf{e}}^{ - st}}f\left( t \right)\,dt}}}}{{1 - {{\bf{e}}^{ - sT}}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.6625em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.8932em;"><span style="top:-2.9052em;"><span class="pstrut" style="height:3.5912em;"></span><span class="mord"><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7673em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.8212em;"><span class="pstrut" style="height:3.5912em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.8932em;"><span class="pstrut" style="height:3.5912em;"></span><span class="mord"><span class="mord"><span class="mop"><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5912em;"><span style="top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight">0</span></span></span></span></span><span style="top:-3.8129em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9119em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8436em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_35" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>35</span></th>
  <td headers="stub_1_35 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>f</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f&#x27;\left( t \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_35 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow><mo>−</mo><mi>f</mi><mrow><mo fence="true">(</mo><mn>0</mn><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">sF\left( s \right) - f\left( 0 \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_36" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>36</span></th>
  <td headers="stub_1_36 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>f</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f&#x27;&#x27;\left( t \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_36 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>s</mi><mn>2</mn></msup><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow><mo>−</mo><mi>s</mi><mi>f</mi><mrow><mo fence="true">(</mo><mn>0</mn><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>f</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mrow><mo fence="true">(</mo><mn>0</mn><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{s^2}F\left( s \right) - sf\left( 0 \right) - f&#x27;\left( 0 \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td></tr>
      <tr><th id="stub_1_37" scope="row" class="gt_row gt_center gt_stub"><span class='gt_from_md'>37</span></th>
  <td headers="stub_1_37 l_time_domain" class="gt_row gt_center" style="background-color: #F2F2F2;"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>f</mi><mrow><mo fence="true">(</mo><mi>n</mi><mo fence="true">)</mo></mrow></msup><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{f^{\left( n \right)}}\left( t \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">(</span></span><span class="mord mathnormal mtight">n</span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">)</span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td>
  <td headers="stub_1_37 l_laplace_s_domain" class="gt_row gt_center"><span class='gt_from_md'><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>s</mi><mi>n</mi></msup><mi>F</mi><mrow><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>s</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>f</mi><mrow><mo fence="true">(</mo><mn>0</mn><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>s</mi><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msup><msup><mi>f</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mrow><mo fence="true">(</mo><mn>0</mn><mo fence="true">)</mo></mrow><mo>⋯</mo><mo>−</mo><mi>s</mi><msup><mi>f</mi><mrow><mo fence="true">(</mo><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow><mo fence="true">)</mo></mrow></msup><mrow><mo fence="true">(</mo><mn>0</mn><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>f</mi><mrow><mo fence="true">(</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo fence="true">)</mo></mrow></msup><mrow><mo fence="true">(</mo><mn>0</mn><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">{s^n}F\left( s \right) - {s^{n - 1}}f\left( 0 \right) - {s^{n - 2}}f&#x27;\left( 0 \right) \cdots - s{f^{\left( {n - 2} \right)}}\left( 0 \right) - {f^{\left( {n - 1} \right)}}\left( 0 \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">s</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord mathnormal">s</span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">(</span></span><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">)</span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">(</span></span><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">)</span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></span></td></tr>
    </tbody>
    <tfoot class="gt_sourcenotes">
      <tr>
        <td class="gt_sourcenote" colspan="3"><span class='gt_from_md'>The hyperbolic functions: <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>cosh</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mo>=</mo><mfrac><mrow><msup><mi mathvariant="bold">e</mi><mi>t</mi></msup><mo>+</mo><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>t</mi></mrow></msup></mrow><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\cosh \left( t \right) = \frac{{{{\bf{e}}^t} + {{\bf{e}}^{ - t}}}}{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cosh</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3482em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0032em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span><span class="mbin mtight">+</span><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span> , <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@<latest>/dist/katex.min.css" data-external="1">
  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sinh</mi><mo>⁡</mo><mrow><mo fence="true">(</mo><mi>t</mi><mo fence="true">)</mo></mrow><mo>=</mo><mfrac><mrow><msup><mi mathvariant="bold">e</mi><mi>t</mi></msup><mo>−</mo><msup><mi mathvariant="bold">e</mi><mrow><mo>−</mo><mi>t</mi></mrow></msup></mrow><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\sinh \left( t \right) = \frac{{{{\bf{e}}^t} - {{\bf{e}}^{ - t}}}}{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">sinh</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">t</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3482em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0032em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight">e</span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td>
      </tr>
    </tfoot>
    <tfoot>
      <tr class="gt_footnotes">
        <td class="gt_footnote" colspan="3">
          <div style="padding-bottom:2px;"><span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;line-height:0;"><sup>1</sup></span> The Heaviside Function. <span class="gt_footnote_marks" style="white-space:nowrap;font-style:italic;font-weight:normal;line-height:0;"><sup>2</sup></span> The Dirac Delta Function.</div>
        </td>
      </tr>
    </tfoot>
  </table>

rstudio/gt documentation built on Feb. 16, 2025, 5:16 p.m.