Multiple-Poly-Bernoulli Polynomials of the Second Kind Associated with Hermite Polynomials

Abstract

Abstract. In this paper, we introduce a new class of Hermite multiple-poly-Bernoulli numbers and polynomials of the second kind and investigate some properties for these polynomials. We derive some implicit summation formulae and general symmetry identities by using different analytical means and applying generating functions. The results derived here are a generalization of some known summation formulae earlier studied by Pathan and Khan.Key words: Hermite polynomials, multi-poly-Bernoulli polynomials of the second kind, Hermite multi-poly-Bernoulli polynomials of the second kind, summation formulae, symmetric identities.

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