Claudio Pita-Ruiz - On bi-variate poly-Bernoulli polynomials

cm:10327 - Communications in Mathematics, November 22, 2022, Volume 31 (2023), Issue 1 -
On bi-variate poly-Bernoulli polynomialsArticle

Authors: Claudio Pita-Ruiz

    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.

    Volume: Volume 31 (2023), Issue 1
    Published on: November 22, 2022
    Accepted on: November 19, 2022
    Submitted on: November 18, 2022
    Keywords: Mathematics - Number Theory,Mathematics - Combinatorics,1B68, 11B73

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