# 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. S : orthopoly1d Chebyshev polynomial of the second kind on $$[-2, 2]$$.

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

 [R414] Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.

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