On the convergence of Hunter's quadrature rule for Cauchy principal value integrals

Hunter's (n+1)-point quadrature rule for the approximate evaluation of the Cauchy principal value integralf1−1 (w(x)f(x)/(x − λ))dx, −1<λ<1, is based on approximatingf by the polynomial which interpolatesf at the pointλ and then zeros of the orthogonal polynomialpn generated by the weight functionw. Sufficient conditions are given to ensure the convergence of a suitably chosen subsequence of the quadrature rules to the integral, whenf is Hölder continuous on [−1,1].