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A class of polynomials and connections with Bernoulli’s numbers

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Abstract

Motivated by certain problems connected with the stochastic analysis of the recursively defined time series, in this paper, we define and study some polynomial sequences. Beside computation of these polynomials and their connection to the Euler–Apostol numbers, we prove some basic properties and give an interesting connection of these polynomials with the well-known Bernoulli numbers, as well as some new summation formulas for Bernoulli’s numbers. Finally, we prove that zeros of these polynomials are simple, real and symmetrically distributed in [0,1].

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Acknowledgements

The authors are deeply grateful to the anonymous referee for his/her suggestions for improvements of the text.

Funding

The first author was supported in part by the Serbian Academy of Sciences and Arts (No. ϕ-96) and the Serbian Ministry of Education, Science and Technological Development (No. #OI 174015).

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Authors and Affiliations

  1. Serbian Academy of Sciences and Arts, Kneza Mihaila 35, Belgrade, 11000, Serbia

    Gradimir V. Milovanović

  2. Faculty of Sciences and Mathematics, University of Niš, Niš, 18000, Serbia

    Gradimir V. Milovanović

  3. Department of Mathematics, Faculty of Science, Akdeniz University, Antalya, Turkey

    Yilmaz Simsek

  4. Department of Mathematics, Faculty of Sciences and Mathematics, University of K. Mitrovica, K. Mitrovica, Serbia

    Vladica S. Stojanović

Authors
  1. Gradimir V. Milovanović
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  2. Yilmaz Simsek
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  3. Vladica S. Stojanović
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Correspondence to Gradimir V. Milovanović.

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Milovanović, G.V., Simsek, Y. & Stojanović, V.S. A class of polynomials and connections with Bernoulli’s numbers. J Anal 27, 709–726 (2019). https://doi.org/10.1007/s41478-018-0116-3

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  • DOI: https://doi.org/10.1007/s41478-018-0116-3

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