Multi-indexed poly-Bernoulli numbers
Abstract
As properties of poly-Bernoulli numbers, a number of formulas such as the duality formula, explicit formula using the Stirling numbers of the second kind and periodicity for negative upper-index have been established. For the multi-indexed poly-Bernoulli numbers generalized by Kaneko-Tsumura, among such properties only the duality formula was obtained. In this paper, we restrict the double-indexed poly-Bernoulli numbers and show the explicit formula using the Stirling numbers of the second kind and periodicity for negative upper-index for them. Further, we define the variant of multiple-indexed poly-Bernoulli numbers using the star-version of multiple-indexed logarithms and obtain the relation between this kind of double and triple-indexed poly-Bernoulli numbers with multi-indexed poly-Bernoulli numbers ahead.
Cite
@article{arxiv.2211.14549,
title = {Multi-indexed poly-Bernoulli numbers},
author = {Yuna Baba and Maki Nakasuji and Mika Sakata},
journal= {arXiv preprint arXiv:2211.14549},
year = {2022}
}