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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 $(x - x^2)^{1/2}$.