bundles / scipy 1.17.1 / scipy / special / _orthogonal / sh_chebyu

function

`scipy.special._orthogonal:sh_chebyu`

source: /scipy/special/_orthogonal.py :2298

Signature

def sh_chebyu ( n , monic = False )

Summary

Shifted Chebyshev polynomial of the second kind.

Extended Summary

Defined as $U_{n}^{*} (x) = U_{n} (2 x - 1)$ for $U_{n}$ the nth Chebyshev polynomial of the second kind.

Parameters

n : int: Degree of the polynomial.
monic : bool, optional: If True, scale the leading coefficient to be 1. Default is False.

Returns

U : orthopoly1d: Shifted Chebyshev polynomial of the second kind.

Notes

The polynomials $U_{n}^{*}$ are orthogonal over $[0, 1]$ with weight function $(x - x^{2})^{1/2}$ .

Aliases

scipy.special.sh_chebyu