期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Ramanujan's cubic transformation and generalized modular equation

Ramanujan's cubic transformation and generalized modular equation
原文传递
导出
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. We study the quotient of hypergeometric functionsμ_a~*(r)=π/2sin(πa) F(a,1-a;1;1-r^3)/F(a,1-a;1;r^3),r∈(0,1)in the theory of Ramanujan's generalized modular equation for a ∈(0,1/2],and find an infinite product formula for μ_(1/3)~*(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.
作者 WANG MiaoKun CHU YuMing SONG YingQing
机构地区 College of Mathematics and Econometrics School of Mathematics and Computation Science
出处 《Science China Mathematics》 SCIE CSCD 2015年第11期2387-2404,共18页 中国科学：数学（英文版）
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)
关键词 Gaussian hypergeometric function Ramanujan＇s cubic transformation generalized modular equa-tion infinite product modular function Ramanujan 广义模块化 立方 超几何函数 方程 变换公式 模块化理论
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献39

  • 1Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. New York: Dover Publications, 1965.
  • 2Anderson G D, Barnard R W, Richards K C, et al. Inequalities for zero-balanced hypergeometric functions. Trans Amer Math Soc, 1995, 347:1713-1723.
  • 3Anderson G D, Qiu S L, Vamanamurthy M K, et al. Generalized elliptic integrals and modular equations. Pacific J Math, 2000, 192:1-37.
  • 4Anderson G D, Vamanamurthy M K, Vuorinen M. Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J Math Anal, 1992, 23:512-524.
  • 5Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Maps. New York: John Wiley g~ Sons, 1997.
  • 6Askey R. Ramanujan and hypergeometric and basic hypergeometric series. In: Ramanujan International Symposium on Analysis. New Delhi: Macmillan of India, 1989, 1-83.
  • 7Baricz Jr. Turin type inequalities for generalized complete elliptic integrals. Math Z, 2007, 256:895-911.
  • 8Baricz A. Landen inequalities for special functions. Proc Amer Math Soc, 2014, 142:3059 3066.
  • 9Barnard R W, Pearce K, Richards K C. A monotonicity property involving 3F2 and comparisons of the classical approximations of elliptical arc length. SIAM J Math Anal, 2000, 32:403-419.
  • 10Baruah N D, Berndt B C. Partition identities and Ramanujan's modular equations. J Combin Theory Ser A, 2007, 114:1024 1045.
Science China Mathematics
2015年 第11期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部