scipy.special.chebys

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

Chebyshev polynomial of the second kind on \([-2, 2]\).

Defined as \(S_n(x) = U_n(x/2)\) where \(U_n\) is the nth Chebychev polynomial of the second kind.

Parameters

nint

Degree of the polynomial.

monicbool, optional

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

Returns

Sorthopoly1d

Chebyshev polynomial of the second kind on \([-2, 2]\).

See also

chebyu

Chebyshev polynomial of the second kind

Notes

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

References

1

Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.

scipy.special.chebyc scipy.special.jacobi