Some modular relations for the G?llnitz-Gordon functions and Ramanujan’s modular equations

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• 作者：Ernest X. W. Xia (1)
  Olivia X. M. Yao (1)
  
• 关键词：Rogers ; Ramanujan functions ; G?llnitz ; Gordon functions ; Ramanujan’s modular equation ; theta functions
• 刊名：Indian Journal of Pure and Applied Mathematics
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：45
• 期：1
• 页码：53-74
• 全文大小：2,352 KB
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  5. A. J. F. Biagioli, A proof of some identities of Ramanujan using modular forms, / Glasg. Math. J., 31 (1989), 271-95. w window">CrossRef
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  7. D. Bressoud, Some identities involving Rogers-Ramanujan-type functions, / J. London Math. Soc., 16 (1977), 9-8. w window">CrossRef
  8. S. L. Chen and S. S. Huang, New modular relations for the G?llnitz-Gordon functions, / J. Number Theory, 93 (2002), 58-5. w window">CrossRef
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• 作者单位：Ernest X. W. Xia (1)
  Olivia X. M. Yao (1)
  
  1. Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang, 212013, P. R. China
  
• ISSN：0975-7465

文摘

Huang used the methods of Rogers, Watson and Bressoud to derive some new modular relations involving the G?llnitz-Gordon functions. In this paper, using Ramanujan’s modular equations, we present a uniform method to prove these modular relations established by Huang.