scipy.special.roots_gegenbauer#

scipy.special.roots_gegenbauer(n, alpha, mu=False)[source]#

Gauss-Gegenbauer quadrature.

Compute the sample points and weights for Gauss-Gegenbauer quadrature. The sample points are the roots of the nth 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 \(w(x) = (1 - x^2)^{\alpha - 1/2}\). See 22.2.3 in [AS] for more details.

Parameters:

nint: quadrature order
alphafloat: alpha must be > -0.5
mubool, optional: If True, return the sum of the weights, optional.

Returns:

xndarray: Sample points
wndarray: Weights
mufloat: Sum of the weights