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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

Author

Listed:
  • Bruce C. Berndt

    (University of Illinois, Department of Mathematics)

  • Atul Dixit

    (University of Illinois, Department of Mathematics)

Abstract

Summary 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.

Suggested Citation

  • Bruce C. Berndt & Atul Dixit, 2010. "A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook," Springer Books, in: Krishnaswami Alladi & John R. Klauder & Calyampudi R. Rao (ed.), The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pages 199-210, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-6263-8_12
    DOI: 10.1007/978-1-4419-6263-8_12
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