{"title":"来自沃森 8φ7 转换的 q-supercongruences","authors":"Xiaoxia Wang, Chang Xu","doi":"10.1515/forum-2023-0409","DOIUrl":null,"url":null,"abstract":"Employing Watson’s <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mmultiscripts> <m:mi>ϕ</m:mi> <m:mn>7</m:mn> <m:none /> <m:mprescripts /> <m:mn>8</m:mn> <m:none /> </m:mmultiscripts> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0409_eq_0156.png\" /> <jats:tex-math>{{}_{8}\\phi_{7}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> transformation formula, we unearth several <jats:italic>q</jats:italic>-supercongruences with a parameter <jats:italic>s</jats:italic>. Particularly, one of our results is an extension of a <jats:italic>q</jats:italic>-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a <jats:italic>q</jats:italic>-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"13 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"q-supercongruences from Watson's 8φ7 transformation\",\"authors\":\"Xiaoxia Wang, Chang Xu\",\"doi\":\"10.1515/forum-2023-0409\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Employing Watson’s <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mmultiscripts> <m:mi>ϕ</m:mi> <m:mn>7</m:mn> <m:none /> <m:mprescripts /> <m:mn>8</m:mn> <m:none /> </m:mmultiscripts> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_forum-2023-0409_eq_0156.png\\\" /> <jats:tex-math>{{}_{8}\\\\phi_{7}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> transformation formula, we unearth several <jats:italic>q</jats:italic>-supercongruences with a parameter <jats:italic>s</jats:italic>. Particularly, one of our results is an extension of a <jats:italic>q</jats:italic>-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a <jats:italic>q</jats:italic>-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.\",\"PeriodicalId\":12433,\"journal\":{\"name\":\"Forum Mathematicum\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-02-20\",\"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-2023-0409\",\"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-2023-0409","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
q-supercongruences from Watson's 8φ7 transformation
Employing Watson’s ϕ78{{}_{8}\phi_{7}} transformation formula, we unearth several q-supercongruences with a parameter s. Particularly, one of our results is an extension of a q-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a q-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.
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.
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