Gegenbauer Functions
The Gegenbauer polynomials are defined in Abramowitz & Stegun, Chapter
22, where they are known as Ultraspherical polynomials. The functions
described in this section are declared in the header file
`gsl_sf_gegenbauer.h'.
- Function: double gsl_sf_gegenpoly_1 (double lambda, double x)
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- Function: double gsl_sf_gegenpoly_2 (double lambda, double x)
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- Function: double gsl_sf_gegenpoly_3 (double lambda, double x)
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- Function: int gsl_sf_gegenpoly_1_e (double lambda, double x, gsl_sf_result * result)
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- Function: int gsl_sf_gegenpoly_2_e (double lambda, double x, gsl_sf_result * result)
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- Function: int gsl_sf_gegenpoly_3_e (double lambda, double x, gsl_sf_result * result)
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These functions evaluate the Gegenbauer polynomials
C^{(\lambda)}_n(x) using explicit
representations for n =1, 2, 3.
- Function: double gsl_sf_gegenpoly_n (int n, double lambda, double x)
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- Function: int gsl_sf_gegenpoly_n_e (int n, double lambda, double x, gsl_sf_result * result)
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These functions evaluate the Gegenbauer polynomial
C^{(\lambda)}_n(x) for a specific value of n,
lambda, x subject to \lambda > -1/2,
n >= 0.
- Function: int gsl_sf_gegenpoly_array (int nmax, double lambda, double x, double result_array[])
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This function computes an array of Gegenbauer polynomials
C^{(\lambda)}_n(x) for n = 0, 1, 2, \dots, nmax, subject
to \lambda > -1/2,
nmax >= 0.