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.
In Memory of Alladi Ramakrishnan
Mathematics Subject Classification (2000) Primary, 11M06; Secondary, 33B15
Research partially supported by grant H98230-07-1-0088 from the National Security Agency.
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Notes
- 1.
The authors are indebted to M. L. Glasser for the proof of this lemma. The authors’ original proof of this lemma was substantially longer than Glasser’s given here.
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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: Alladi, K., Klauder, J., Rao, C. (eds) The Legacy of Alladi Ramakrishnan in the Mathematical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6263-8_12
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