scipy.special.sh_chebyu¶

scipy.special.sh_chebyu(n, monic=False)[source]

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
nint

Degree of the polynomial.

monicbool, optional

If True, scale the leading coefficient to be 1. Default is False.

Returns
Uorthopoly1d

Shifted Chebyshev polynomial of the second kind.

Notes

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

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