scipy.special.sh_chebyt

scipy.special.sh_chebyt(n, monic=False)

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:

n : int

Degree of the polynomial.

monic : bool, optional

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

Returns:

T : orthopoly1d

Shifted Chebyshev polynomial of the first kind.

Notes

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