{"title":"Lauricella超几何函数FD的一些变换公式","authors":"Keiji Matsumoto, Katsuyoshi Ohara","doi":"10.1619/FESI.52.203","DOIUrl":null,"url":null,"abstract":"In this paper, we give some functional equations with a parameter c for Lauricella’s hypergeometric functions; they can be regarded as multivariable versions of the Gauss quadratic transformation formula for the hypergeometric function. These functional equations for c = 1 are utilized for the study of arithmetic-geometric means of several terms.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":"53 1","pages":"203-212"},"PeriodicalIF":0.7000,"publicationDate":"2009-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Some transformation formulas for Lauricella's hypergeometric functions FD\",\"authors\":\"Keiji Matsumoto, Katsuyoshi Ohara\",\"doi\":\"10.1619/FESI.52.203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give some functional equations with a parameter c for Lauricella’s hypergeometric functions; they can be regarded as multivariable versions of the Gauss quadratic transformation formula for the hypergeometric function. These functional equations for c = 1 are utilized for the study of arithmetic-geometric means of several terms.\",\"PeriodicalId\":55134,\"journal\":{\"name\":\"Funkcialaj Ekvacioj-Serio Internacia\",\"volume\":\"53 1\",\"pages\":\"203-212\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2009-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Funkcialaj Ekvacioj-Serio Internacia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1619/FESI.52.203\",\"RegionNum\":4,\"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":"Funkcialaj Ekvacioj-Serio Internacia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1619/FESI.52.203","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some transformation formulas for Lauricella's hypergeometric functions FD
In this paper, we give some functional equations with a parameter c for Lauricella’s hypergeometric functions; they can be regarded as multivariable versions of the Gauss quadratic transformation formula for the hypergeometric function. These functional equations for c = 1 are utilized for the study of arithmetic-geometric means of several terms.
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