5.7.2.11.45. scipy.special.u_roots¶

scipy.special.u_roots(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 n-th 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 $f(x) = \sqrt{1 - x^2}$.

Parameters:	n : int quadrature order mu : bool, optional If True, return the sum of the weights, optional.
Returns:	x : ndarray Sample points w : ndarray Weights mu : float Sum of the weights

See also

scipy.integrate.quadrature, scipy.integrate.fixed_quad