Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

Bruce C. Berndt, George Lamb, Mathew Rogers

Research output: Contribution to journalArticlepeer-review

Abstract

We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers-Ramanujan continued fraction play central roles in our evaluations.

Original languageEnglish (US)
Pages (from-to)185-198
Number of pages14
JournalRamanujan Journal
Volume29
Issue number1-3
DOIs
StatePublished - Dec 2012

Keywords

  • Class invariants
  • Cubic continued fraction
  • Hypergeometric functions
  • Jacobian elliptic functions
  • Ramanujan's theta functions
  • Rogers-Ramanujan continued fraction
  • Singular moduli
  • Two-dimensional lattice sums

ASJC Scopus subject areas

  • Algebra and Number Theory

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