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Introduction and Preliminaries

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Series of Bessel and Kummer-Type Functions

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Abstract

We begin with a brief outline of special functions and methods, which will be needed in the next chapters. We recall here briefly the Gamma, Beta, Digamma functions, Pochhammer symbol, Bernoulli polynomials and numbers, Bessel, modified Bessel, generalized hypergeometric, Fox–Wright generalized hypergeometric, Hurwitz–Lerch Zeta functions, the Euler–Maclaurin summation formula together with Dirichlet series and Cahen’s formula, Mathieu series, Bessel and Struve differential equations, Fourier-Bessel and Dini series of Bessel functions and fractional differintegral.

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Notes

  1. 1.

    Here, and in what follows χ A (x) denotes the indicator function of the set A which equals 1, when x ∈ A, and zero else.

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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

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Baricz, Á., Jankov Maširević, D., Pogány, T.K. (2017). Introduction and Preliminaries. 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_1

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