scipy.special.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: n : int Degree of the polynomial. monic : bool, optional If True, scale the leading coefficient to be 1. Default is False. T : orthopoly1d Shifted Chebyshev polynomial of the first kind.

Notes

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

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