# 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:
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 $$[-2, 2]$$.

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.