Abstract
We show that the error term of every modified compound quadrature rule for Cauchy principal value integrals with degree of exactnesss is of optimal order of magnitude in the classesC k [−1,1],k=1,2,...,s, but not inCs+1[−1,1]. We give explicit upper bounds for the error constants of the modified midpoint rule, the modified trapezoidal rule and the modified Simpson rule. Furthermore, the results are generalized to analogous rules for Hadamard-type finite part integrals.
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