Description Usage Arguments Value Examples
Calculates the value of
Γ_1(x, α) = \int_x^∞ t^{α-1} e^{-it} \mathrm{d}t
for 0 < α < 1 through the following relations:
\int_0^∞ t^{α-1} e^{-it} \mathrm{d}t = e^{-i\frac{π}{2}α} \int_0^∞ t^{α-1} e^{-t} \mathrm{d}t = e^{-i\frac{π}{2}α} Γ(α).
obtained by contour integration, and:
\int_0^x t^{α-1} e^{-it} \mathrm{d}t = \int_0^x t^{α-1} \mathrm{cos}(t) \mathrm{d}t - i \int_0^x t^{α-1} \mathrm{sin}(t) \mathrm{d}t = Ci(x, α) - i Si(x, α)
. The first integral is calculated using function "tgamma" from the library "boost::math", while the functions Ci and Si are approximated via Taylor expansions.
1 | inc_gamma_imag(x, alpha)
|
x |
A non-negative number |
alpha |
A number between 0 and 1 (strictly) |
The incomplete gamma function of imaginary argument (see Details)
1 | inc_gamma_imag(1.0, 0.5)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.