scipy.special.eval_gegenbauer¶

scipy.special.eval_gegenbauer(n, alpha, x, out=None) = <ufunc 'eval_gegenbauer'>¶

Evaluate Gegenbauer polynomial at a point.

The Gegenbauer polynomials can be defined via the Gauss hypergeometric function \({}_2F_1\) as

\[C_n^{(\alpha)} = \frac{(2\alpha)_n}{\Gamma(n + 1)} {}_2F_1(-n, 2\alpha + n; \alpha + 1/2; (1 - z)/2).\]

When \(n\) is an integer the result is a polynomial of degree \(n\).

Parameters:	n : array_like Degree of the polynomial. If not an integer, the result is determined via the relation to the Gauss hypergeometric function. alpha : array_like Parameter x : array_like Points at which to evaluate the Gegenbauer polynomial
Returns:	C : ndarray Values of the Gegenbauer polynomial