# 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: n : int Degree of the polynomial. monic : bool, optional If True, scale the leading coefficient to be 1. Default is False. U : orthopoly1d Shifted Chebyshev polynomial of the second kind.

Notes

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

#### Previous topic

scipy.special.sh_chebyt

#### Next topic

scipy.special.sh_jacobi