Numerical integration in the presence of an interior singularity

摘要

The convergence of sequences of integration rules applied to an improperly integrable function with an interior singularity is investigated. The rules studied include the Gauss-Jacobi rules and the interpolatory integration rules based on the zeros of (1 − x2)mPn−2m(α,β)(x), m0, 1 for certain values of α and β. The results are then applied to the study of the convergence of Hunter's method for Cauchy principal value integrals.