scipy.special.roots_chebyu¶
-
scipy.special.
roots_chebyu
(n, mu=False)[source]¶ Gauss-Chebyshev (second kind) quadrature.
Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the nth degree Chebyshev polynomial of the second kind, \(U_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-1, 1]\) with weight function \(w(x) = \sqrt{1 - x^2}\). See 22.2.5 in [AS] for details.
- Parameters
- nint
quadrature order
- mubool, optional
If True, return the sum of the weights, optional.
- Returns
- xndarray
Sample points
- wndarray
Weights
- mufloat
Sum of the weights
References
- AS
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.