ChebPoly: Evaluates the Chebyshev nth order polynomial of the first...

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Evaluates the Chebyshev nth order polynomial of the first kind

Description

ChebPoly(n, x) evaluates the Chebyshev nth order polynomial of the first kind T_n(x), where T_n(x) = cos(n*acos(x)).

Usage

ChebPoly(n, x)

Arguments

n	order of polynomial.
x	points, in which we want to compute the value of polynomial.

Value

Function returns values of nth order Chebysev polynomial of the first kind evaluated in points x.

Note

Ver.: 01-Oct-2018 12:33:49 (consistent with Matlab CharFunTool v1.3.0, 07-Sep-2017 16:20:17).

See Also

For more details see also https://en.wikipedia.org/wiki/Chebyshev_polynomials.

Other Utility Function: ChebCoefficients(), ChebPoints(), ChebPolyValues(), ChebValues(), GammaLog(), GammaMultiLog(), GammaMulti(), GammaZX(), Hypergeom1F1MatApprox(), Hypergeom1F1Mat(), Hypergeom2F1Mat(), Hypergeom2F1(), HypergeompFqMat(), InterpChebValues(), hypergeom1F1(), interpBarycentric()

Examples

## EXAMPLE 1
n <- 0:5
x <- ChebPoints(32, c(-1, 1))
pval <- ChebPoly(n, x[[1]])
matplot(x[[1]], t(pval),
        main = 'Chebyshev polynomials T_n(x) evaluated at Chebyshev points',
        type = "l")

gajdosandrej/CharFunToolR documentation built on June 3, 2024, 7:46 p.m.