Certain integrals arising from Ramanujan's notebooks

Bruce C. Berndt, Armin Straub

Research output: Contribution to journalArticlepeer-review


In his third notebook, Ramanujan claims that (Formula Presented) In a following cryptic line, which only became visible in a recent reproduction of Ramanujan's notebooks, Ramanujan indicates that a similar relation exists if log x were replaced by log2 x in the first integral and log x were inserted in the integrand of the second integral. One of the goals of the present paper is to prove this claim by contour integration. We further establish general theorems similarly relating large classes of infinite integrals and illustrate these by several examples.

Original languageEnglish (US)
Article number093
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - Oct 14 2015


  • Contour integration
  • Ramanujan's notebooks
  • Trigonometric integrals

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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