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 \([-2, 2]\).
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
- 1
Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.