{"title":"New interesting Euler sums","authors":"A. Nimbran, A. Sofo","doi":"10.7153/jca-2019-15-02","DOIUrl":null,"url":null,"abstract":". We present here some new and interesting Euler sums obtained by means of related integrals and elementary approach. We supplement Euler’s general recurrence formula with two general formulas of the form ∑ n (cid:2) 1 O ( m ) n (cid:2) 1 ( 2 n − 1 ) p + 1 ( 2 n ) p (cid:3) and ∑ n (cid:2) 1 O n ( 2 n − 1 ) p ( 2 n + 1 ) q , where O ( m ) n = n ∑ j = 1 1 ( 2 j − 1 ) m . Two formulas for ζ ( 5 ) are also derived.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of classical analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/jca-2019-15-02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
. We present here some new and interesting Euler sums obtained by means of related integrals and elementary approach. We supplement Euler’s general recurrence formula with two general formulas of the form ∑ n (cid:2) 1 O ( m ) n (cid:2) 1 ( 2 n − 1 ) p + 1 ( 2 n ) p (cid:3) and ∑ n (cid:2) 1 O n ( 2 n − 1 ) p ( 2 n + 1 ) q , where O ( m ) n = n ∑ j = 1 1 ( 2 j − 1 ) m . Two formulas for ζ ( 5 ) are also derived.
． 我们现在呈现出一些新的和有趣的欧拉sums我们一起supplement欧拉公式的将军recurrence二将军formulas∑n (cid》没有注明:2 O (m) n (cid) 1: 2) 1 (n−1)p n + 1 (2) p (cid: 3)和∑n (cid 2) 1 O n (n−1)p (n + 1) q,在O (m) n = n∑j j = 1号(2−1)m。为ζ(5)是两个formulas也derived。
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