Poly-Bernoulli Numbers and Polynomials

Abstract

In this paper we consider some generalizations of Poly-Bernoulli numbers and Poly-Bernoulli Poynomials. The generalization is by means of Polylogarithimic functions, Stirling numbers and via weighted Stirling numbers. All these generalizations lead to symmetries between various types of Stirling numbers, and enable us to investigate and expand algebraic proper ties of Poly-Bernoulli numbers and polynomials. We also combine these generalizations and derive numerous combinatorial and arithmetical identities.