{"title":"柯西数和斯特林数的新级数，第二部分","authors":"K. Boyadzhiev, L. Kargin","doi":"10.2298/aadm210112001b","DOIUrl":null,"url":null,"abstract":"We evaluate in closed form several series involving products of Cauchy\n numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic,\n and central binomial). Similar results are obtained with series involving\n Stirling numbers of the first kind. We focus on several particular cases\n which give new closed forms for Euler sums of hyperharmonic numbers and\n products of hyperharmonic and harmonic numbers.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"New series with Cauchy and Stirling numbers, Part 2\",\"authors\":\"K. Boyadzhiev, L. Kargin\",\"doi\":\"10.2298/aadm210112001b\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We evaluate in closed form several series involving products of Cauchy\\n numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic,\\n and central binomial). Similar results are obtained with series involving\\n Stirling numbers of the first kind. We focus on several particular cases\\n which give new closed forms for Euler sums of hyperharmonic numbers and\\n products of hyperharmonic and harmonic numbers.\",\"PeriodicalId\":51232,\"journal\":{\"name\":\"Applicable Analysis and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-03-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Analysis and Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2298/aadm210112001b\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/aadm210112001b","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
New series with Cauchy and Stirling numbers, Part 2
We evaluate in closed form several series involving products of Cauchy
numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic,
and central binomial). Similar results are obtained with series involving
Stirling numbers of the first kind. We focus on several particular cases
which give new closed forms for Euler sums of hyperharmonic numbers and
products of hyperharmonic and harmonic numbers.
期刊介绍：
Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).
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