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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:

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

[R391]

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