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