Generalized Bessel functions and Kapteyn series

G. Dattoli, A. Torre, S. Lorenzutta, G. Maino

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Kapteyn series are introduced for generalized Bessel functions in full analogy with ordinary Bessel functions. Apart from the relevance that Kapteyn series have in astronomical problems and in electromagnetic radiation theory, interest in this type of series is justified by the possibility of expanding analytic functions of a complex variable in series of Bessel functions with specific features. Accordingly, in this paper, it is shown that it is possible to obtain expansions of m-variable analytic functions in series of GBF's, which reproduce the structure of Kapteyn series of ordinary Bessel functions. The possible field of applications is also suggested.
Original languageEnglish
Pages (from-to)117 - 125
Number of pages9
JournalComputers and Mathematics with Applications
Issue number8
Publication statusPublished - 1998
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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