Acta Mathematica Hungarica

, Volume 141, Issue 3, pp 254–281 | Cite as

Integral representations and summations of the modified Struve function

Article

Abstract

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.

Key words and phrases

modified Struve function Bessel function and modified Bessel function of the first kind Neumann, Kapteyn and Schlömilch series of modified Bessel and Struve functions Dirichlet series Cahen formula generalized hypergeometric function Struve differential equation 

Mathematics Subject Classification

33C10 33E20 40H05 30B50 40C10 65B10 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Department of EconomicsBabeş–Bolyai UniversityCluj-NapocaRomania
  2. 2.Faculty of Maritime StudiesUniversity of RijekaRijekaCroatia

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