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<p>In this article, we develop Ramanujan’s theory of elliptic functions to the cubic base using Jacobi’s theta functions. Our new approach does not involve the theta series discovered by J. M. Borwein and P. B. Borwein, Goursat’s transformation formulas for the hypergeometric series, analogue of Gauss’ AGM and the theory of modular forms.</p>

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Ramanujan’s Theory of Elliptic Functions to the Cubic Base

  • 期刊论文

  • 发表日期：

    2025年4月2日

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  • Heng Huat Chan,
  • Zhi-Guo Liu

摘要

In this article, we develop Ramanujan’s theory of elliptic functions to the cubic base using Jacobi’s theta functions. Our new approach does not involve the theta series discovered by J. M. Borwein and P. B. Borwein, Goursat’s transformation formulas for the hypergeometric series, analogue of Gauss’ AGM and the theory of modular forms.