Integral representations and summations of the modified Struve function

Árpád Baricz, Tibor K. Pogány

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7 Citations (Scopus)


It is known that the Struve function H ν and the modified Struve function L ν are closely connected to the Bessel function of the first kind J ν and to the modified Bessel function of the first kind I ν and possess representations through higher transcendental functions like the generalized hypergeometric 1 F 2 and the Meijer G function. Also, the NIST project and Wolfram formula collection contain a set of Kapteyn type series expansions for L ν(x). In this paper firstly, we obtain various another type integral representation formulae for L ν(x) using the technique developed by D. Jankov and the authors. Secondly, we present some summation results for different kind of Neumann, Kapteyn and Schlömilch series built by I ν(x) and L ν(x) which are connected by a Sonin-Gubler formula, and by the associated modified Struve differential equation. Finally, solving a Fredholm type convolutional integral equation of the first kind, Bromwich-Wagner line integral expressions are derived for the Bessel function of first kind J ν and for an associated generalized Schlömilch series.

Original languageEnglish
Pages (from-to)254-281
Number of pages28
JournalActa Mathematica Hungarica
Issue number3
Publication statusPublished - Nov 1 2013



  • 30B50
  • 33C10
  • 33E20
  • 40C10
  • 40H05
  • 65B10
  • Bessel function and modified Bessel function of the first kind
  • Cahen formula
  • Dirichlet series
  • Neumann, Kapteyn and Schlömilch series of modified Bessel and Struve functions
  • Struve differential equation
  • generalized hypergeometric function
  • modified Struve function

ASJC Scopus subject areas

  • Mathematics(all)

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