SciPy

scipy.special.chebys

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

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:

n : int

Degree of the polynomial.

monic : bool, optional

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

Returns:

S : orthopoly1d

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

[R349]Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.

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