A transformation formula involving the Gamma and Riemann zeta functions in Ramanujan's Lost Notebook

2009/04/07 by Bruce C. Berndt, Berndt, Bruce C., Atul Dixit +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.0904.1053

Abstract

In 'The Lost Notebook and Other Unpublished Papers' of Ramanujan are present some manuscripts of Ramanujan in the handwriting of G. N. Watson which are 'copied from loose papers'. We present a proof of a beautiful formula of Ramanujan in one of these manuscripts, namely a transformation formula involving the Gamma function and Riemann Zeta function. This formula elegantly yields a modular relation. Later we also give another proof of the first equality of this transformation formula along the lines suggested by Andrew P. Guinand.

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