{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2009-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1619/FESI.52.203\",\"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/10.1619/FESI.52.203","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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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