Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

B. J. Stoyanov, R. A. Farrell, J. F. Bird

Research output: Contribution to journalArticle

Abstract

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann-Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods - a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.

Original languageEnglish (US)
Pages (from-to)533-543
Number of pages11
JournalJournal of Computational and Applied Mathematics
Volume50
Issue number1-3
DOIs
StatePublished - May 20 1994

Keywords

  • Asymptotic expansion
  • Bessel functions
  • Generalized hypergeometric function
  • Hankel integral
  • Meijer function
  • Riemann-Liouville integral

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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