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scipy.special.roots_gegenbauer

scipy.special.roots_gegenbauer(n, alpha, mu=False)

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