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scipy.special.j_roots

scipy.special.j_roots(n, alpha, beta, mu=False)[source]

Gauss-Jacobi quadrature.

Computes the sample points and weights for Gauss-Jacobi quadrature. The sample points are the roots of the n-th degree Jacobi polynomial, Pα,βn(x). These sample points and weights correctly integrate polynomials of degree 2n1 or less over the interval [1,1] with weight function f(x)=(1x)α(1+x)β.

Parameters:

n : int

quadrature order

alpha : float

alpha must be > -1

beta : float

beta must be > 0

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