FULLY DEGENERATE HERMITE POLY-BERNOULLI NUMBERS AND POLYNOMIALS

Abstract

In the paper, we first introduce the fully degenerate Hermite poly-Bernoulli polynomials and investigate their properties. Next we derive the implicit summation formulae and general symmetry identities by making use of different analytical means and generating function method. The results obtained here are the corresponding generalizations of some known summations and identities on the fully degenerate Hermite poly-Bernoulli numbers and polynomials.