scipy.special.sh_chebyu

scipy.special.sh_chebyu(n, monic=False)

Shifted Chebyshev polynomial of the second kind.

Defined as \(U^*_n(x) = U_n(2x - 1)\) 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 \((x - x^2)^{1/2}\).