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A Sequence of Polynomials Generated by a Kapteyn Series of the Second Kind

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Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra

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Abstract

In this paper, we find an explicit representation for a Kapteyn series of the second kind in terms of a family of polynomials Pn(x). We also use symbolic computation methods to find a recurrence relation that allows fast calculation of the coefficients of Pn(x).

Dedicated to Peter Paule, friend and mentor. Thank you for sharing your insight and enthusiasm.

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Acknowledgements

The first author was supported by the strategic program “Innovatives OÖ– 2010 plus” from the Upper Austrian Government. The second author was partly funded by the Austrian Science Fund (FWF): W1214-N15 and under the grant SFB F50-07. We would like to thank the anonymous referees for valuable suggestions.

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Authors and Affiliations

  1. Johannes Kepler University Linz, Doktoratskolleg, “Computational Mathematics”, Linz, Austria

    Diego Dominici

  2. Department of Mathematics State University of New York at New Paltz, New Paltz, NY, USA

    Diego Dominici

  3. Johannes Kepler University Linz, RISC, Linz, Austria

    Veronika Pillwein

Authors
  1. Diego Dominici
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  2. Veronika Pillwein
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Correspondence to Diego Dominici .

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Editors and Affiliations

  1. Research Institut for Symbolic Computation, Johannes Kepler University of Linz, Linz, Oberösterreich, Austria

    Veronika Pillwein

  2. Research Institut for Symbolic Computation, Johannes Kepler University of Linz, Linz, Austria

    Carsten Schneider

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Dominici, D., Pillwein, V. (2020). A Sequence of Polynomials Generated by a Kapteyn Series of the Second Kind. In: Pillwein, V., Schneider, C. (eds) Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra. Texts & Monographs in Symbolic Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-44559-1_9

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  • DOI: https://doi.org/10.1007/978-3-030-44559-1_9

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