{"title":"涉及二重、三重和四重和的罗杰斯-拉马努扬式等差数列","authors":"Zhi Li, Liuquan Wang","doi":"10.1007/s11139-024-00901-x","DOIUrl":null,"url":null,"abstract":"<p>We prove a number of new Rogers–Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the literature. This is achieved by direct summation or the constant term method. We also obtain some new single-sum identities as consequences.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"55 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rogers–Ramanujan type identities involving double, triple and quadruple sums\",\"authors\":\"Zhi Li, Liuquan Wang\",\"doi\":\"10.1007/s11139-024-00901-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove a number of new Rogers–Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the literature. This is achieved by direct summation or the constant term method. We also obtain some new single-sum identities as consequences.</p>\",\"PeriodicalId\":501430,\"journal\":{\"name\":\"The Ramanujan Journal\",\"volume\":\"55 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-12\",\"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/s11139-024-00901-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00901-x","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
我们证明了一些新的罗杰斯-拉马努扬类型的等式，涉及二重、三重和四重和。它们是在使用 Maple 进行广泛搜索后发现的。证明的主要思路是将它们还原为文献中的一些已知等式。这是通过直接求和或常数项法实现的。作为结果，我们还得到了一些新的单和等式。
Rogers–Ramanujan type identities involving double, triple and quadruple sums
We prove a number of new Rogers–Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the literature. This is achieved by direct summation or the constant term method. We also obtain some new single-sum identities as consequences.
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