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 \(n\). See 22.5.46 in [AS] for details. - Parameters:
- narray_like
- Degree of the polynomial. If not an integer, the result is determined via the relation to the Gauss hypergeometric function. 
- alphaarray_like
- Parameter 
- xarray_like
- Points at which to evaluate the Gegenbauer polynomial 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- Cscalar or ndarray
- Values of the Gegenbauer polynomial 
 
 - See also - roots_gegenbauer
- roots and quadrature weights of Gegenbauer polynomials 
- gegenbauer
- Gegenbauer polynomial object 
- hyp2f1
- Gauss hypergeometric function 
 - References [AS]- Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.