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Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem

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Abstract

It is shown in this paper, by making use of contour integration and the Cauchy integral theorem, that two general families of definite integrals can be evaluated in closed form and are expressible only in terms of the Hurwitz zeta function and elementary functions. In addition, a number of interesting (known or new) special cases and consequences of the main results are considered and some comparison with results of symbolic computation is made.

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Authors and Affiliations

  1. Atomic Physics Laboratory, Vinča Institute of Nuclear Sciences, P.O. Box 522, YU-11001, Belgrade, Serbia

    Djurdje Cvijović

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada

    H. M. Srivastava

Authors
  1. Djurdje Cvijović
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  2. H. M. Srivastava
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Correspondence to H. M. Srivastava.

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Dedicated to the memory of Professor Luigi Gatteschi (1923–2007).

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Cvijović, D., Srivastava, H.M. Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem. Numer Algor 49, 129–141 (2008). https://doi.org/10.1007/s11075-008-9158-y

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  • DOI: https://doi.org/10.1007/s11075-008-9158-y

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