Gegenbauer Functions
The Gegenbauer polynomials are defined in Abramowitz & Stegun,
Chapter 22, where they are known as Ultraspherical polynomials.
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gsl_sf_gegenpoly_1(lambda, x)
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gsl_sf_gegenpoly_2(lambda, x)
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gsl_sf_gegenpoly_3(lambda, x)
These functions evaluate the Gegenbauer polynomials \(C^{(\lambda)}_n(x)\)
using explicit representations for \(n = 1, 2, 3\).
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gsl_sf_gegenpoly_n(n, lambda, x)
This function evaluates the Gegenbauer polynomial \(C^{(\lambda)}_n(x)\)
for a specific value of \(n\), \(\lambda\), \(x\) subject to \(\lambda > -1/2\),
\(n \geq 0\).