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gegenbauer
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x^2)^(α–1/2). They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer.
Computes the Gegenbauer polynomial with order n, parameter alpha at the point z.
Argument n
Scalar
Argument alpha
Scalar
Argument z
Scalar
Returns 1. entry
Scalar
gegenbauer(0, 1, 0.5)
The 0th order polynomial is always 1.0.
gegenbauer(1, 0.5, 0.25)
Computes the 1st order polynomial with parameter alpha = 0.5 at the point 0.25, which gives us -0.25.
Computes the Gegenbauer polynomial with order n, parameter alpha at the points in Z.
Argument n
Scalar
Argument alpha
Scalar
Argument Z
Matrix
Returns 1. entry
Matrix
gegenbauer(1, 1, 0:0.1:1)
The 0th order polynomial is always 1.0.