Preprint Article Version 1 This version is not peer-reviewed

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)

A peer-reviewed article of this Preprint also exists.

Journal reference: Advanced Studies in Contemporary Mathematics 2018, 28, 285-296
DOI: 10.17777/ascm2018.28.2.296


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 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.

Subject Areas

Hermite-Kampé de Fériet polynomials; Hermite Bernoulli polynomials; poly Bernoulli polynomials; Stirling numbers of second kind; Polylogarithm functions.

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