On bi-variate poly-Bernoulli polynomials

A Note on Degenerate Hermite Poly–bernoulli Numbers and Polynomials

In this paper, we introduce a new class of degenerate Hermite poly-Bernoulli polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of d...

A new class of generalized Laguerre-based poly-Bernoulli polynomials

A new class of generalized Laguerre-based poly-Bernoulli polynomials are discussed with an attempt to generate new and interesting identities, some are in relation with Stirling number of the second kind. Different analytical means and generating function method is incorporated to derive implicit summation formulae and symmetry identities for generalized Laguerre poly-Bernoulli polynomials. It ...

The Arakawa–kaneko Zeta Function and Poly-bernoulli Polynomials

The purpose of this paper is to introduce a generalization of the Arakawa–Kaneko zeta function and investigate their special values at negative integers. The special values are written as the sums of products of Bernoulli and poly-Bernoulli polynomials. We establish the basic properties for this zeta function and their special values.

Hermite based poly-Bernoulli polynomials with a q-parameter

Ugur Duran, Mehmet Acikgoz and Serkan Araci Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey E-Mail: [email protected] Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey E-Mail: [email protected] Department of Economics, Faculty of Economics, Administrative and Social Scienc...

Bernoulli polynomials