scipy.special.

roots_sh_jacobi#

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

Gauss-Jacobi (shifted) quadrature.

Compute the sample points and weights for Gauss-Jacobi (shifted) quadrature. The sample points are the roots of the nth 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 \(w(x) = (1 - x)^{p-q} x^{q-1}\). See 22.2.2 in [AS] for details.

Parameters:

nint: quadrature order
p1float: (p1 - q1) must be > -1
q1float: q1 must be > 0
mubool, optional: If True, return the sum of the weights, optional.

Returns:

xndarray: Sample points
wndarray: Weights
mufloat: Sum of the weights