{"title":"7 F 6 超几何变换公式产生的超级共轭关系","authors":"Chen Wang","doi":"10.1515/forum-2023-0239","DOIUrl":null,"url":null,"abstract":"Using a <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mmultiscripts> <m:mi>F</m:mi> <m:mn>6</m:mn> <m:none /> <m:mprescripts /> <m:mn>7</m:mn> <m:none /> </m:mmultiscripts> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0239_eq_0198.png\" /> <jats:tex-math>{{}_{7}F_{6}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> hypergeometric transformation formula, we prove two supercongruences. In particular, one of these supercongruences confirms a recent conjecture of Guo, Liu and Schlosser, and gives an extension of a supercongruence of Long and Ramakrishna.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"180 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Supercongruences arising from a 7 F 6 hypergeometric transformation formula\",\"authors\":\"Chen Wang\",\"doi\":\"10.1515/forum-2023-0239\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Using a <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mmultiscripts> <m:mi>F</m:mi> <m:mn>6</m:mn> <m:none /> <m:mprescripts /> <m:mn>7</m:mn> <m:none /> </m:mmultiscripts> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_forum-2023-0239_eq_0198.png\\\" /> <jats:tex-math>{{}_{7}F_{6}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> hypergeometric transformation formula, we prove two supercongruences. In particular, one of these supercongruences confirms a recent conjecture of Guo, Liu and Schlosser, and gives an extension of a supercongruence of Long and Ramakrishna.\",\"PeriodicalId\":12433,\"journal\":{\"name\":\"Forum Mathematicum\",\"volume\":\"180 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum Mathematicum\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/forum-2023-0239\",\"RegionNum\":3,\"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":"Forum Mathematicum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/forum-2023-0239","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
利用 F 6 7 {{}_{7}F_{6}} 超几何变换公式，我们证明了两个超级共轭。其中一个超共轭证实了郭，刘和施洛瑟最近的猜想，并给出了龙和拉马克里希纳的超共轭的扩展。
Supercongruences arising from a 7 F 6 hypergeometric transformation formula
Using a F67{{}_{7}F_{6}} hypergeometric transformation formula, we prove two supercongruences. In particular, one of these supercongruences confirms a recent conjecture of Guo, Liu and Schlosser, and gives an extension of a supercongruence of Long and Ramakrishna.
期刊介绍：
Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
