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With existing numerical integration methods and algorithms it is difficult in general to obtain accurate approximations to integrals of the formwhere f is a sufficiently smooth function on [0, 1]. Gautschi has developed software (as scripts in Matlab) for computing these integrals for the special case r = ω = 1. In this paper, an algorithm (as a Mathematica program) is developed for computing these integrals to arbitrary precision for any given values of the parameters in a certain range. Numerical examples are given of testing the performance of the algorithm/program.

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