Jacobi-Gauss quadrature, also called Jacobi quadrature or Mehler quadrature, is a Gaussian quadrature over the interval with weighting function
(1)
|
The abscissas for quadrature order are given by the roots of the Jacobi polynomials . The weights are
(2)
| |||
(3)
|
where is the coefficient of in . For Jacobi polynomials,
(4)
|
where is a gamma function. Additionally,
(5)
|
so
(6)
| |||
(7)
|
where
(8)
|
The error term is
(9)
|
(Hildebrand 1956).