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Second Type Neumann Series of Generalized Nicholson Function

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Abstract

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.

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Notes

  1. Here, and in what follows [a] and \( \{a\}=a-[a]\) stand for the integer and fractional part of certain real a, respectively.

  2. Here, and in what follows \(\chi _A\) denotes the characteristic function of the set A.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, University of Osijek, Osijek, 31000, Croatia

    Dragana Jankov Maširević

  2. Faculty of Maritime Studies, University of Rijeka, Rijeka, 51000, Croatia

    Tibor K. Pogány

  3. Institute of Applied Mathematics, Óbuda University, Budapest, 1034, Hungary

    Tibor K. Pogány

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  1. Dragana Jankov Maširević
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  2. Tibor K. Pogány
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Correspondence to Dragana Jankov Maširević.

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Jankov Maširević, D., Pogány, T.K. Second Type Neumann Series of Generalized Nicholson Function. Results Math 75, 12 (2020). https://doi.org/10.1007/s00025-019-1138-0

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