A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook

Bruce C. Berndt () and Atul Dixit ()
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Bruce C. Berndt: University of Illinois, Department of Mathematics
Atul Dixit: University of Illinois, Department of Mathematics

A chapter in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, 2010, pp 199-210 from Springer

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.

Keywords: Ramanujan’s Lost Notebook; Gamma function; Riemann zeta function; Riemann Ξ-function (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6263-8_12

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DOI: 10.1007/978-1-4419-6263-8_12

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