Polylogarithms and poly-Bernoulli polynomials. (English) Zbl 1268.11030
Summary: In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. We call them poly-Bernoulli polynomials. We prove a collection of extremely important and fundamental identities satisfied by our poly-Bernoulli polynomials and numbers. These properties are of arithmetical nature.
MSC:
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 11A07 | Congruences; primitive roots; residue systems |
| 11M41 | Other Dirichlet series and zeta functions |
