5.7.2.11.33. scipy.special.cg_roots¶

scipy.special.cg_roots(n, alpha, mu=False)[source]¶

Gauss-Gegenbauer quadrature.

Computes the sample points and weights for Gauss-Gegenbauer quadrature. The sample points are the roots of the n-th degree Gegenbauer polynomial, $C^{\alpha}_n(x)$. These sample points and weights correctly integrate polynomials of degree $2n - 1$ or less over the interval $[-1, 1]$ with weight function $f(x) = (1 - x^2)^{\alpha - 1/2}$.

Parameters:	n : int quadrature order alpha : float alpha must be > -0.5 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