# scipy.special.chebyu¶

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

Chebyshev polynomial of the second kind.

Defined to be the solution of

$(1 - x^2)\frac{d^2}{dx^2}U_n - 3x\frac{d}{dx}U_n + n(n + 2)U_n = 0;$

$$U_n$$ is a polynomial of degree $$n$$.

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

chebyt
Chebyshev polynomial of the first kind.

Notes

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

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