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scipy.special.js_roots

scipy.special.js_roots(n, p1, q1, mu=False)[source]

Gauss-Jacobi (shifted) quadrature.

Computes the sample points and weights for Gauss-Jacobi (shifted) quadrature. The sample points are the roots of the n-th degree shifted Jacobi polynomial, Gp,qn(x). These sample points and weights correctly integrate polynomials of degree 2n1 or less over the interval [0,1] with weight function f(x)=(1x)pqxq1

Parameters:

n : int

quadrature order

p1 : float

(p1 - q1) must be > -1

q1 : float

q1 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

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