Convergence acceleration of Jacobi-Gauss quadrature formulae for analytic functions with poles

Let (Sn) be the sequence given by the Jacobi-Gauss quadrature method when the integrand is an analytic function with different kinds of poles located outside the interval of integration, and S its limit. We give an asymptotic representation of the errors S − Sn and of Sn+1 − Sn, which leads to build other sequences which give a better approximation of the exact value of the integral than Sn. All the results are illustrated by numerical examples.