Further convergence results for two quadrature rules for Cauchy type principal value integrals

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New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Holder condition with exponent less or equal to $\frac12$. The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules.