Generalizations of Poly-Bernoulli numbers and polynomials

Abstract

The Concepts of poly-Bernoulli numbers $B_n^{(k)}$, poly-Bernoulli polynomials $B_n^k(t)$ and the generalized poly-bernoulli numbers $B_n^{(k)}(a,b)$ are generalized to $B_n^{(k)}(t,a,b,c)$ which is called the generalized poly-Bernoulli polynomials depending on real parameters \textit{a,b,c}. Some properties of these polynomials and some relationships between $B_n^k$, $B_n^{(k)}(t)$, $B_n^{(k)}(a,b)$ and $B_n^{(k)}(t,a,b,c)$ are established

10 pages