10.46298/cm.10327
https://cm.episciences.org/10327
Pita-Ruiz, Claudio
Claudio
Pita-Ruiz
On bi-variate poly-Bernoulli polynomials
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.
episciences.org
Mathematics - Number Theory
Mathematics - Combinatorics
1B68, 11B73
CC0 1.0 Universal (CC0 1.0) Public Domain Dedication
2022-11-19
2022-11-22
2022-11-22
eng
journal article
arXiv:2211.09278
10.48550/arXiv.2211.09278
2336-1298
https://cm.episciences.org/10327/pdf
VoR
application/pdf
Communications in Mathematics
Volume 31 (2023), Issue 1
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