Gessel和Stanton超几何求和公式的推论和多重推广

IF 0.3 Q4 MATHEMATICS Acta et Commentationes Universitatis Tartuensis de Mathematica Pub Date : 2021-06-21 DOI:10.12697/acutm.2021.25.02

T. Ernst, P. W. Karlsson

{"title":"Gessel和Stanton超几何求和公式的推论和多重推广","authors":"T. Ernst, P. W. Karlsson","doi":"10.12697/acutm.2021.25.02","DOIUrl":null,"url":null,"abstract":"We find some new simple hypergeometric formulas in the footsteps of the important article by Gessel and Stanton. These are multiple reduction formulas, multiple summation formulas, as well as multiple transformation formulas for special Kampé de Fériet functions and Appell functions. The hypergeometric summation formulas have special function arguments in Q and parameter values in N or C. The proofs use Pfaff-Kummer transformation, Euler transformation, or an improved form of Slater reversion.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"41 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Corollaries and multiple extensions of Gessel and Stanton hypergeometric summation formulas\",\"authors\":\"T. Ernst, P. W. Karlsson\",\"doi\":\"10.12697/acutm.2021.25.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We find some new simple hypergeometric formulas in the footsteps of the important article by Gessel and Stanton. These are multiple reduction formulas, multiple summation formulas, as well as multiple transformation formulas for special Kampé de Fériet functions and Appell functions. The hypergeometric summation formulas have special function arguments in Q and parameter values in N or C. The proofs use Pfaff-Kummer transformation, Euler transformation, or an improved form of Slater reversion.\",\"PeriodicalId\":42426,\"journal\":{\"name\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-06-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12697/acutm.2021.25.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta et Commentationes Universitatis Tartuensis de Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12697/acutm.2021.25.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们从格塞尔和斯坦顿的重要文章中找到了一些新的简单的超几何公式。这些是多个约简公式，多个求和公式，以及特殊kamp de fsamriet函数和Appell函数的多个变换公式。超几何求和公式在Q上有特殊的函数参数，在N或c上有特殊的参数值。证明采用了Pfaff-Kummer变换、Euler变换或Slater反演的改进形式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Corollaries and multiple extensions of Gessel and Stanton hypergeometric summation formulas

We find some new simple hypergeometric formulas in the footsteps of the important article by Gessel and Stanton. These are multiple reduction formulas, multiple summation formulas, as well as multiple transformation formulas for special Kampé de Fériet functions and Appell functions. The hypergeometric summation formulas have special function arguments in Q and parameter values in N or C. The proofs use Pfaff-Kummer transformation, Euler transformation, or an improved form of Slater reversion.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊