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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 2n−1 or less over the interval [−1,1] with weight function f(x)=(1−x)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