On bi-variate poly-Bernoulli polynomials

Pita-Ruiz, Claudio

doi:10.46298/cm.10327

On bi-variate poly-Bernoulli polynomials

Journal

Communications in Mathematics

ISSN

2336-1298

Date Issued

2022

Author(s)

Pita-Ruiz, Claudio

Facultad de Ingeniería - CampCM

Type

text::journal::journal article

DOI

10.46298/cm.10327

URL

https://scripta.up.edu.mx/handle/20.500.12552/4978

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.