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

Returns

Cndarray

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.

scipy.special.eval_hermitenorm scipy.special.eval_sh_legendre