scipy.special.roots_gegenbauer(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 \(f(x) = (1 - x^2)^{\alpha - 1/2}\).


n : int

quadrature order

alpha : float

alpha must be > -0.5

mu : bool, optional

If True, return the sum of the weights, optional.


x : ndarray

Sample points

w : ndarray


mu : float

Sum of the weights