Abstract
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 polynomialp n 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 Holder continuous on [−1,1].
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