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scipy.special.chebyu

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

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.

Returns:

U : orthopoly1d

Chebyshev polynomial of the second kind.

See also

chebyt

Chebyshev polynomial of the first kind.

Notes

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