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Hermite based Poly-Bernoulli Polynomials with a q-parameter
Version 1
: Received: 19 February 2018 / Approved: 22 February 2018 / Online: 22 February 2018 (15:28:12 CET)
How to cite: Duran, U.; Acikgoz, M.; Araci, S. Hermite based Poly-Bernoulli Polynomials with a q-parameter. Preprints 2018, 2018020145. https://doi.org/10.20944/preprints201802.0145.v1 Duran, U.; Acikgoz, M.; Araci, S. Hermite based Poly-Bernoulli Polynomials with a q-parameter. Preprints 2018, 2018020145. https://doi.org/10.20944/preprints201802.0145.v1
Abstract
We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give someof their basic properties including not only addition property, but also derivative properties and integralrepresentations. We also de.ne the Hermite based λ -Stirling polynomials of the second kind, and thenprovide some relations. Moreover, we derive several correlations and identities including the Hermite-Kampéde Fériet (or Gould-Hopper) family of polynomials, the Hermite based poly-Bernoulli polynomials with a qparameter and the Hermite based λ -Stirling polynomials of the second kind.
Keywords
Hermite-Kampé de Fériet polynomials; Hermite Bernoulli polynomials; poly Bernoulli polynomials; Stirling numbers of second kind; Polylogarithm functions.
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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