A transformation formula involving the gamma and riemann zeta functions in Ramanujan's lost notebook

Bruce C. Berndt, Atul Dixit

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Two proofs are given for a series transformation formula involving the logarithmic derivative of the Gamma function found in Ramanujan's lost notebook. The transformation formula is connected with a certain integral embodying the Riemann zeta function that is similar to integrals examined by Ramanujan in his one published paper on the zeta function.

Original languageEnglish (US)
Title of host publicationThe Legacy of Alladi Ramakrishnan in the Mathematical Sciences
PublisherSpringer New York
Pages199-210
Number of pages12
ISBN (Print)9781441962621
DOIs
StatePublished - Jan 1 2010

Keywords

  • Gamma function
  • Ramanujan's lost notebook
  • Riemann zeta function
  • Riemann Ξ-function

ASJC Scopus subject areas

  • Mathematics(all)

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    Berndt, B. C., & Dixit, A. (2010). A transformation formula involving the gamma and riemann zeta functions in Ramanujan's lost notebook. In The Legacy of Alladi Ramakrishnan in the Mathematical Sciences (pp. 199-210). Springer New York. https://doi.org/10.1007/978-1-4419-6263-8_12