Results in Mathematics

, 75:12 | Cite as

Second Type Neumann Series of Generalized Nicholson Function

  • Dragana Jankov MaširevićEmail author
  • Tibor K. Pogány


The second type Neumann series are considered whose building blocks are generalized Nicholson’s functions \(B_\nu ^p(x) :=J_\nu ^p(x)+ Y_\nu ^p(x)\), being \(J_\nu , Y_\nu \) Bessel functions of the first and second kind of order \(\nu \), \(p \ge 2\) integer. Closed form definite integral expressions are obtained for such series with the aid of the associated Dirichlet series’ Cahen’s Laplace integral form.


Bessel functions of the first and second kind modified Bessel function of the second kind \(K_\nu \) Nicholson function Neumann series of Bessel functions Cahen’s Laplace integral formula 

Mathematics Subject Classification

Primary 33C10 33E20 40C10 Secondary 33E30 40H05 



The authors are indebted to both unknown referees for several constructive comments which mainly improve the exposition’s relevance and completeness and finally encompass the article. T.K. Pogány acknowledges the support given by the NAWA project PROM PPI/PRO/2018/1/00008 and thanks to the Department of Mathematical Physics, The Henryk Niewodniczański Institute of Nuclear Physics of Polish Academy of Sciences, Kraków, Poland for the warm hospitality and the excellent working atmosphere during his stay there during February 2019.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Dragana Jankov Maširević
    • 1
    Email author
  • Tibor K. Pogány
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of OsijekOsijekCroatia
  2. 2.Faculty of Maritime StudiesUniversity of RijekaRijekaCroatia
  3. 3.Institute of Applied MathematicsÓbuda UniversityBudapestHungary

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