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SciPy

This is documentation for an old release of SciPy (version 0.19.0). Read this page in the documentation of the latest stable release (version 1.15.1).

scipy.special.eval_jacobi

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

Evaluate Jacobi polynomial at a point.

The Jacobi polynomials can be defined via the Gauss hypergeometric function 2F1 as

P(α,β)n(x)=(α+1)nΓ(n+1)2F1(n,1+α+β+n;α+1;(1z)/2)

where ()n is the Pochhammer symbol; see poch. 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

beta : array_like

Parameter

x : array_like

Points at which to evaluate the polynomial

Returns:

P : ndarray

Values of the Jacobi polynomial

See also

roots_jacobi
roots and quadrature weights of Jacobi polynomials
jacobi
Jacobi polynomial object
hyp2f1
Gauss hypergeometric function