{"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":18282,"journal":{"name":"Mathematica Slovaca","volume":"44 1","pages":""},"PeriodicalIF":0.9000,"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\":18282,\"journal\":{\"name\":\"Mathematica Slovaca\",\"volume\":\"44 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Slovaca\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2024-0048\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0048","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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