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 $${}_2F_1$$ as

$P_n^{(\alpha, \beta)}(x) = \frac{(\alpha + 1)_n}{\Gamma(n + 1)} {}_2F_1(-n, 1 + \alpha + \beta + n; \alpha + 1; (1 - z)/2)$

where $$(\cdot)_n$$ is the Pochhammer symbol; see poch. When $$n$$ is an integer the result is a polynomial of degree $$n$$. See 22.5.42 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

betaarray_like

Parameter

xarray_like

Points at which to evaluate the polynomial

Returns
Pndarray

Values of the Jacobi polynomial

roots_jacobi

roots and quadrature weights of Jacobi polynomials

jacobi

Jacobi 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.

Previous topic

scipy.special.eval_chebys

Next topic

scipy.special.eval_laguerre