{"title":"AN ALTERNATE CIRCULAR SUMMATION FORMULA OF THETA FUNCTIONS AND ITS APPLICATIONS","authors":"Jun-Ming Zhu","doi":"10.2298/AADM120204004Z","DOIUrl":null,"url":null,"abstract":"We prove a general alternate circular summation formula of theta functions, \n which implies a great deal of theta-function identities. In particular, we \n recover several identities in Ramanujan's Notebook from this identity. We \n also obtain two formulaes for (q; q)2n∞.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"6 1","pages":"114-125"},"PeriodicalIF":1.0000,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2298/AADM120204004Z","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/AADM120204004Z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 7
Abstract
We prove a general alternate circular summation formula of theta functions,
which implies a great deal of theta-function identities. In particular, we
recover several identities in Ramanujan's Notebook from this identity. We
also obtain two formulaes for (q; q)2n∞.
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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