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