An integral analogue of theta functions and gauss sums in Ramanujan's lost notebook

Bruce C. Berndt, Ping Xu

Research output: Contribution to journalArticlepeer-review

Abstract

One page in Ramanujan's lost notebook is devoted to claims about a certain integral with two parameters. One claim gives an inversion formula for the integral that is similar to the transformation formula for theta functions. Other claims are remindful of Gauss sums. In this paper we prove all the claims made by Ramanujan about this integral.

Original languageEnglish (US)
Pages (from-to)257-265
Number of pages9
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume147
Issue number2
DOIs
StatePublished - Sep 2009

ASJC Scopus subject areas

  • General Mathematics

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