On the convergence of spline product quadratures for Cauchy principal value integrals (Q1177200)

The paper studies the convergence of product integration formulas that evaluate Cauchy principal value integrals of the form \(\int u(x)f(x)/(x- \lambda)dx\) by approximating \(f\) with a cubic spline. Convergence is established, and convergence rates obtained, when \(f\) is Hölder continuous of order \(\mu\), \(0<\mu\leq 1\). If \(u\) is a Jacobi weight the convergence is uniform in \(\lambda\) for suitable values of \(\mu\).