sh_chebyt#

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

Shifted Chebyshev polynomial of the first kind.

Defined as $T^*_n(x) = T_n(2x - 1)$ for $T_n$ the nth Chebyshev polynomial of the first kind.

Parameters:

nint

Degree of the polynomial.

monicbool, optional

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

Returns:

Torthopoly1d

Shifted Chebyshev polynomial of the first kind.

Notes

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