{"docId":10327,"paperId":10327,"url":"https:\/\/cm.episciences.org\/10327","doi":"10.46298\/cm.10327","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":673,"name":"Volume 31 (2023), Issue 1"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"2211.09278","repositoryVersion":2,"repositoryLink":"https:\/\/arxiv.org\/abs\/2211.09278v2","dateSubmitted":"2022-11-18 17:09:00","dateAccepted":"2022-11-19 13:53:29","datePublished":"2022-11-22 11:45:24","titles":["On bi-variate poly-Bernoulli polynomials"],"authors":["Pita-Ruiz, Claudio"],"abstracts":["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."],"keywords":["Mathematics - Number Theory","Mathematics - Combinatorics","1B68, 11B73"]}