2022/11/26 by Yuna Baba, Baba, Yuna, Maki Nakasuji +3
Mathematics · Medicine · #11B68 #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Intraocular Surgery and Lenses #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2211.14549
openalex publication_date 2022/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.