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Multi Poly-Bernoulli and Multi Poly-Euler Polynomials

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Applied Mathematical Analysis: Theory, Methods, and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 177))

Abstract

In this chapter, a certain variation of Bernoulli and Euler numbers and polynomials is introduced by means of polylogarithm, particularly, the poly-Bernoulli and Euler numbers and polynomials. Furthermore, a certain generalization of poly-Bernoulli and poly-Euler numbers and polynomials is defined by means of multiple polylogarithm. Common properties shared by the family of Bernoulli and Euler numbers and polynomials are discussed including recurrence relations, explicit formulas and several identities expressing these generalizations in terms of the other special numbers and functions (e.g. Stirling numbers and their generalizations).

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Authors and Affiliations

  1. Department of Mathematics, Cebu Normal University, 6000, Cebu City, Philippines

    Roberto B. Corcino

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  1. Roberto B. Corcino
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Correspondence to Roberto B. Corcino .

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Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  2. Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

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Corcino, R.B. (2020). Multi Poly-Bernoulli and Multi Poly-Euler Polynomials. In: Dutta, H., Peters, J. (eds) Applied Mathematical Analysis: Theory, Methods, and Applications. Studies in Systems, Decision and Control, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-99918-0_21

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