{"title":"涉及奇次谐波数和二项式系数的和的求值","authors":"W. Zheng, Y. Yang","doi":"10.1007/s10476-024-00011-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we extend tools developed in [9] to study Euler <i>T</i>-type sums involving odd harmonic numbers and binomial coefficients. In particular, we will prove that two kinds of Euler <i>T</i>-type sums can be expressed in terms of log(2), zeta values, double <i>T</i>-values, (odd) harmonic numbers and double <i>T</i>-sums.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Evaluations of sums involving odd harmonic numbers and binomial coefficients\",\"authors\":\"W. Zheng, Y. Yang\",\"doi\":\"10.1007/s10476-024-00011-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we extend tools developed in [9] to study Euler <i>T</i>-type sums involving odd harmonic numbers and binomial coefficients. In particular, we will prove that two kinds of Euler <i>T</i>-type sums can be expressed in terms of log(2), zeta values, double <i>T</i>-values, (odd) harmonic numbers and double <i>T</i>-sums.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-024-00011-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-024-00011-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文扩展了 [9] 中开发的工具,以研究涉及奇次谐波数和二项式系数的欧拉 T 型和。特别是,我们将证明有两种欧拉 T 型和可以用 log(2)、zeta 值、双 T 值、(奇)谐波数和双 T 和来表示。
Evaluations of sums involving odd harmonic numbers and binomial coefficients
In this paper, we extend tools developed in [9] to study Euler T-type sums involving odd harmonic numbers and binomial coefficients. In particular, we will prove that two kinds of Euler T-type sums can be expressed in terms of log(2), zeta values, double T-values, (odd) harmonic numbers and double T-sums.