{"title":"Generalizations of Rogers–Ramanujan type identities","authors":"Li-Jun Hao, Xueya Kuai, Lan Xia","doi":"10.1007/s11139-024-00918-2","DOIUrl":null,"url":null,"abstract":"<p>Recently the integral method was widely used to prove some Nahm problems. In the present paper we apply this method and the three-term transformation formula for <span>\\({}_2\\phi _1\\)</span> series to establish some multi-sum Rogers-Ramanujan type identities with parameters. As special cases, we derive known Rogers-Ramanujan type identities, also find some new identities.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"99 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00918-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Recently the integral method was widely used to prove some Nahm problems. In the present paper we apply this method and the three-term transformation formula for \({}_2\phi _1\) series to establish some multi-sum Rogers-Ramanujan type identities with parameters. As special cases, we derive known Rogers-Ramanujan type identities, also find some new identities.
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