Product integration of singular integrands using Hermite-Feje´r interpolation

Conditions are given onk andf for the convergence of product integration ofkf based on Hermite-Fejer polynomials interpolatingf at the zeros of Jacobi polynomials and possibly one or both endpoints of the integration interval. Iff has endpoint singularities, we can ignore the singularity. An interior singularity must generally be avoided.