scipy.special.j_roots

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

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, \(P^{\alpha, \beta}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-1, 1]\) with weight function \(f(x) = (1 - x)^{\alpha} (1 + x)^{\beta}\).

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

See also

scipy.integrate.quadrature, scipy.integrate.fixed_quad