scipy.special._orthogonal:roots_jacobi

Extended Summary

Compute the sample points and weights for Gauss-Jacobi quadrature. The sample points are the roots of the nth degree Jacobi polynomial, $P_n^{\alpha ,\beta }(x)$. These sample points and weights correctly integrate polynomials of degree $2n-1$ or less over the interval $[-1,1]$ with weight function $w(x)=(1-x{)}^{\alpha }(1+x{)}^{\beta }$. See 22.2.1 in [AS] for details.