scipy.special.chebyu¶
-
scipy.special.
chebyu
(n, monic=False)[source]¶ Chebyshev polynomial of the second kind.
Defined to be the solution of
\[(1 - x^2)\frac{d^2}{dx^2}U_n - 3x\frac{d}{dx}U_n + n(n + 2)U_n = 0;\]\(U_n\) is a polynomial of degree \(n\).
- Parameters
- nint
Degree of the polynomial.
- monicbool, optional
If True, scale the leading coefficient to be 1. Default is False.
- Returns
- Uorthopoly1d
Chebyshev polynomial of the second kind.
See also
chebyt
Chebyshev polynomial of the first kind.
Notes
The polynomials \(U_n\) are orthogonal over \([-1, 1]\) with weight function \((1 - x^2)^{1/2}\).