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The Ramanujan Journal

, Volume 46, Issue 1, pp 189–200 | Cite as

Inequalities and infinite product formula for Ramanujan generalized modular equation function

  • Miao-Kun Wang
  • Yong-Min Li
  • Yu-Ming Chu
Article

Abstract

We present several inequalities for the Ramanujan generalized modular equation function \(\mu _{a}(r)=\pi F(a,1-a;1;1-r^2)/\) \([2\sin (\pi a)F(a,1-a;1;r^2)]\) with \(a\in (0,1/2]\) and \(r\in (0,1)\), and provide an infinite product formula for \(\mu _{1/4}(r)\), where \(F(a,b;c;x)={}_{2}F_{1}(a,b;c;x)\) is the Gaussian hypergeometric function.

Keywords

Gaussian hypergeometric function Ramanujan generalized modular equation Quadratic transformation Infinite product 

Mathematics Subject Classification

33C05 11F03 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsHuzhou UniversityHuzhouChina

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