Ramanujan's cubic transformation and generalized modular equation

作     者：WANG MiaoKun CHU YuMing SONG YingQing 

作者机构：College of Mathematics and EconometricsHunan University School of Mathematics and Computation ScienceHunan City University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2015年第58卷第11期

页      面：2387-2404页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11371125,11171307 and 61374086) Natural Science Foundation of Zhejiang Province(Grant No.LY13A010004) Natural Science Foundation of Hunan Province(Grant No.12C0577) PhD Students Innovation Foundation of Hunan Province(Grant No.CX2012B153) 

主　　题：Gaussian hypergeometric function Ramanujan's cubic transformation generalized modular equa-tion infinite product modular function 

摘      要：We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.