Multi-indexed poly-Bernoulli numbers
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...
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| creator | Baba, Yuna Nakasuji, Maki Sakata, Mika |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2211.14549 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.2211.14549</identifier><language>eng</language><subject>Mathematics - Number Theory</subject><creationdate>2022-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2211.14549$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2211.14549$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Baba, Yuna</creatorcontrib><creatorcontrib>Nakasuji, Maki</creatorcontrib><creatorcontrib>Sakata, Mika</creatorcontrib><title>Multi-indexed poly-Bernoulli numbers</title><description>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.</description><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrsKwjAUgOEsDqI-gJMOrqnNtcmo4g0UB93LSXMKgVglWtG3Fy_Tv_18hAxZnkmjVD6F9AyPjHPGMiaVtF0y2bfxHmhoPD7Rj6-X-KJzTM2ljTGMm_bsMN36pFNDvOHg3x45rpanxYbuDuvtYrajoAtLK13VhdfGGu6cywUYj2ic5BqMZVJjXSnwUiFowQst0KGyKIGBNqZyokdGv-tXWV5TOEN6lR9t-dWKN-oCOj0</recordid><startdate>20221126</startdate><enddate>20221126</enddate><creator>Baba, Yuna</creator><creator>Nakasuji, Maki</creator><creator>Sakata, Mika</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20221126</creationdate><title>Multi-indexed poly-Bernoulli numbers</title><author>Baba, Yuna ; Nakasuji, Maki ; Sakata, Mika</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-c6cf7d68982bbb03a8dee8b426a89146efc5ad45ea632763ebe59e4a1a688cb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Baba, Yuna</creatorcontrib><creatorcontrib>Nakasuji, Maki</creatorcontrib><creatorcontrib>Sakata, Mika</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Baba, Yuna</au><au>Nakasuji, Maki</au><au>Sakata, Mika</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multi-indexed poly-Bernoulli numbers</atitle><date>2022-11-26</date><risdate>2022</risdate><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.</abstract><doi>10.48550/arxiv.2211.14549</doi><oa>free_for_read</oa></addata></record> |
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| title | Multi-indexed poly-Bernoulli numbers |
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