Integrals associated with Ramanujan and elliptic functions

Bruce C. Berndt

Research output: Contribution to journalArticlepeer-review


We evaluate in closed form certain classes of infinite integrals containing trigonometric and hyperbolic trigonometric functions in their integrands. Although not apparent, the integrals are related to Jacobian elliptic functions, in particular, to theorems found in Ramanujan’s notebooks. One of our evaluations answers a question first posed by M. E. H. Ismail.

Original languageEnglish (US)
Pages (from-to)369-389
Number of pages21
JournalRamanujan Journal
Issue number1-3
StatePublished - Nov 1 2016


  • Definite integrals
  • Jacobian elliptic functions
  • Ramanujan’s notebooks

ASJC Scopus subject areas

  • Algebra and Number Theory


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