scipy.special.chebys¶
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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
[R403] Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.