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arXiv · 2211.14549

Multi-indexed poly-Bernoulli numbers

Yuna Baba·Maki Nakasuji·Mika Sakata
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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.

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Yuna Baba, Maki Nakasuji, Mika Sakata. 2022-11-26. Multi-indexed poly-Bernoulli numbers. https://arxiv.org/abs/2211.14549

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