Integrals of Lipschitz–Hankel type, Legendre functions and table errata

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3 Scopus citations

Abstract

ABSTRACT: The complete Lipschitz–Hankel integrals (LHIs) include the Laplace transforms of the Bessel functions, multiplied by powers. Such Laplace transforms can be evaluated using associated Legendre functions. It is noted that there are errors in published versions of these evaluations, and a merged and emended list of seven transforms is given. Errata for standard reference works, such as the table of Gradshteyn and Ryzhik, are also given. Most of the errors are attributable to inconsistent normalization of the Legendre functions. These transforms can be viewed as limits of incomplete LHIs, which find application in communication theory.

Original languageEnglish (US)
Pages (from-to)385-391
Number of pages7
JournalIntegral Transforms and Special Functions
Volume27
Issue number5
DOIs
StatePublished - May 3 2016

Keywords

  • Bessel function
  • Ferrers function
  • Laplace transform
  • Lipschitz–Hankel integral
  • associated Legendre function
  • integral transform
  • table errata

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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