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.