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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, Cαn(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−x2)α−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