{"title":"范哈姆（F.2）超共融和一些相关超共融的新 q-analogues","authors":"Qiuxia Hu","doi":"10.1515/ms-2024-0048","DOIUrl":null,"url":null,"abstract":"In terms of a very-well-poised <jats:sub>6</jats:sub> <jats:italic>ϕ</jats:italic> <jats:sub>5</jats:sub> summation formula, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we establish four new <jats:italic>q</jats:italic>-supercongruences for truncated basic hypergeometric series. One of these results is a new <jats:italic>q</jats:italic>-analogue of the (F.2) supercongruence of Van Hamme.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences\",\"authors\":\"Qiuxia Hu\",\"doi\":\"10.1515/ms-2024-0048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In terms of a very-well-poised <jats:sub>6</jats:sub> <jats:italic>ϕ</jats:italic> <jats:sub>5</jats:sub> summation formula, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we establish four new <jats:italic>q</jats:italic>-supercongruences for truncated basic hypergeometric series. One of these results is a new <jats:italic>q</jats:italic>-analogue of the (F.2) supercongruence of Van Hamme.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2024-0048\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
In terms of a very-well-poised 6ϕ5 summation formula, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we establish four new q-supercongruences for truncated basic hypergeometric series. One of these results is a new q-analogue of the (F.2) supercongruence of Van Hamme.
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