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.