scipy.special.roots_sh_jacobi

scipy.special.roots_sh_jacobi(n, p1, q1, mu=False)

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, \(G^{p,q}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, 1]\) with weight function \(f(x) = (1 - x)^{p-q} x^{q-1}\)

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

See also

scipy.integrate.quadrature, scipy.integrate.fixed_quad