On bi-variate poly-Bernoulli polynomials
Number Theory
2023-06-22 v2 Combinatorics
Abstract
We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on standard Bernoulli polynomials, as the addition formula and the binomial formula. We also prove a result that allows us to obtain poly-Bernoulli polynomial identities from polynomial identities, and we use this result to obtain several identities involving products of poly-Bernoulli and/or standard Bernoulli polynomials. We prove two generalized recurrences for bi-variate poly-Bernoulli polynomials, and obtain some corollaries from them.
Cite
@article{arxiv.2211.09278,
title = {On bi-variate poly-Bernoulli polynomials},
author = {Claudio Pita-Ruiz},
journal= {arXiv preprint arXiv:2211.09278},
year = {2023}
}