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A Few Theta-Function Identities and Some of Ramanujan's Modular Equations

Abstract

We prove three modular equations of Ramanujan using theta-function identities. Proofs via methods known to Ramanujan were not available hitherto. One had previously been proved by classical methods, and two had been proved using the theory of modular forms.

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Baruah, N.D. A Few Theta-Function Identities and Some of Ramanujan's Modular Equations. The Ramanujan Journal 4, 239–250 (2000). https://doi.org/10.1023/A:1009835301693

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  • DOI: https://doi.org/10.1023/A:1009835301693

  • theta-function
  • elliptic integral
  • modulus
  • modular equation
  • multiplier