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

nint

Degree of the polynomial.

monicbool, optional

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

Returns

Uorthopoly1d

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