Neumann Series

  • Árpád Baricz
  • Dragana Jankov Maširević
  • Tibor K. Pogány
Part of the Lecture Notes in Mathematics book series (LNM, volume 2207)


The goal of present chapter is to study in details the integral representations of the Neumann series (of the first and second type) of Bessel and modified Bessel functions of the first and second kind. In order to achieve our goal we use several methods: the Euler–Maclaurin summation technique, differential equation technique, fractional integration technique. Moreover, we present some interesting results on the coefficients of Neumann series, product of modified Bessel functions of the first and second kind and the cumulative distribution function of the non-central χ2-distribution.


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Authors and Affiliations

  • Árpád Baricz
    • 1
    • 2
  • Dragana Jankov Maširević
    • 3
  • Tibor K. Pogány
    • 1
    • 4
  1. 1.John von Neumann Faculty of Informatics, Institute of Applied MathematicsÓbuda UniversityBudapestHungary
  2. 2.Department of EconomicsBabeş–Bolyai UniversityCluj–NapocaRomania
  3. 3.Department of MathematicsJosip Juraj Strossmayer University of OsijekOsijekCroatia
  4. 4.Faculty of Maritime StudiesUniversity of RijekaRijekaCroatia

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