bundles / scipy 1.17.1 / scipy / special / _orthogonal / sh_jacobi

function

`scipy.special._orthogonal:sh_jacobi`

source: /scipy/special/_orthogonal.py:461

Signature

def sh_jacobi(n, p, q, monic = False)

Summary

Shifted Jacobi polynomial.

Extended Summary

Defined by

G_{n}^{(p, q)} (x) = (n 2 n + p - 1)^{- 1} P_{n}^{(p - q, q - 1)} (2 x - 1),

where $P_{n}^{(\cdot, \cdot)}$ is the nth Jacobi polynomial.

Parameters

n : int: Degree of the polynomial.
p : float: Parameter, must have $p > q - 1$ .
q : float: Parameter, must be greater than 0.
monic : bool, optional: If True, scale the leading coefficient to be 1. Default is False.

Returns

G : orthopoly1d: Shifted Jacobi polynomial.

Notes

For fixed $p, q$ , the polynomials $G_{n}^{(p, q)}$ are orthogonal over $[0, 1]$ with weight function $(1 - x)^{p - q} x^{q - 1}$ .

Aliases

scipy.special.sh_jacobi