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Series of Bessel and Kummer-Type Functions pp 87–111Cite as

Kapteyn Series

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2207))

Abstract

In this chapter we deduce several results for Kapteyn series of Bessel and Kummer hypergeometric functions. We present some integral representations and results on coefficients by using the Euler-Maclaurin summation technique and the differential equation technique.

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Notes

  1. 1.

    In fact Exton applied the inequality \(J_{N+2k}\big \{ (N+2k)z\big \} \leq 1,\, N+2k\in \mathbb N_0\) such that didn’t appear in [333], but which one readily follows by Hansen’s bounds (3.5).

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Authors and Affiliations

  1. John von Neumann Faculty of Informatics, Institute of Applied Mathematics, Óbuda University, Budapest, Hungary

    Árpád Baricz & Tibor K. Pogány

  2. Department of Economics, Babeş–Bolyai University, Cluj–Napoca, Romania

    Árpád Baricz

  3. Department of Mathematics, Josip Juraj Strossmayer University of Osijek, Osijek, Croatia

    Dragana Jankov Maširević

  4. Faculty of Maritime Studies, University of Rijeka, Rijeka, Croatia

    Tibor K. Pogány

Authors
  1. Árpád Baricz
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  2. Dragana Jankov Maširević
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  3. Tibor K. Pogány
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Baricz, Á., Jankov Maširević, D., Pogány, T.K. (2017). Kapteyn Series. In: Series of Bessel and Kummer-Type Functions. Lecture Notes in Mathematics, vol 2207. Springer, Cham. https://doi.org/10.1007/978-3-319-74350-9_3

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