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Evaluation of classes of definite integrals involving elementary functions via differentiation of special functions

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Herein, it is shown that by exploiting integral definitions of well known special functions, through generalizations and differentiations, broad classes of definite integrals can be solved in closed form or in terms of special functions. This is especially useful when there is no closed form solution to the indefinite form of the integral. In this paper, three such classes of definite integrals are presented. Two of these classes incorporate and supercede all of Kölbig's integration formulae [11], including his formulation for the computation of Cauchy principal values. Also presented are the mathematical derivations that support the implementation of a third class which exploits the incomplete Gamma function. The resulting programs, based on pattern matching, differentiation, and occasionally limits, are very efficient.

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Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    K. O. Geddes

  2. Department of Physics and Department of Mathematics and Computer Science, Clarkson University, 13676, Potsdam, New York, USA

    M. L. Glasser

  3. Guelph-Waterloo Program for Graduate Work in Physics, Waterloo Campus, USA

    R. A. Moore & T. C. Scott

  4. the Institute for Theoretical Atomic and Molecular Physics at the Harvard—Smithsonian Center for Astrophysics, 60 Garden Street, 02138, Cambridge, MA, USA

    T. C. Scott

Authors
  1. K. O. Geddes
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  2. M. L. Glasser
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  3. R. A. Moore
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  4. T. C. Scott
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As of September 1990

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Geddes, K.O., Glasser, M.L., Moore, R.A. et al. Evaluation of classes of definite integrals involving elementary functions via differentiation of special functions. AAECC 1, 149–165 (1990). https://doi.org/10.1007/BF01810298

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  • DOI: https://doi.org/10.1007/BF01810298

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