Applicable Algebra in Engineering, Communication and Computing

, Volume 1, Issue 2, pp 149–165

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


  • K. O. Geddes
    • Department of Computer ScienceUniversity of Waterloo
  • M. L. Glasser
    • Department of Physics and Department of Mathematics and Computer ScienceClarkson University
  • R. A. Moore
    • Guelph-Waterloo Program for Graduate Work in PhysicsWaterloo Campus
  • T. C. Scott
    • Guelph-Waterloo Program for Graduate Work in PhysicsWaterloo Campus
    • the Institute for Theoretical Atomic and Molecular Physics at the Harvard—Smithsonian Center for Astrophysics

DOI: 10.1007/BF01810298

Cite this article as:
Geddes, K.O., Glasser, M.L., Moore, R.A. et al. AAECC (1990) 1: 149. doi:10.1007/BF01810298


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.


IntegrationSymbolic ComputationMAPLESpecial Functions
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© Springer-Verlag 1990