{"title":"A new explicit formula for Bernoulli numbers involving the Euler number","authors":"S. Jha","doi":"10.31219/osf.io/zkwjc","DOIUrl":null,"url":null,"abstract":"In this brief note, we derive a new explicit formula for Bernoulli numbers in terms of the Stirling numbers of the second kind and the Euler numbers. As a corollary of our result, we obtain an explicit formula for the Euler numbers in terms of the Stirling numbers of the second kind.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow Journal of Combinatorics and Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31219/osf.io/zkwjc","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 6
Abstract
In this brief note, we derive a new explicit formula for Bernoulli numbers in terms of the Stirling numbers of the second kind and the Euler numbers. As a corollary of our result, we obtain an explicit formula for the Euler numbers in terms of the Stirling numbers of the second kind.
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