Ramanujan's formula for the logarithmic derivative of the gamma function

Details Ramanujan's formula for the logarithmic derivative of the gamma function Ramanujan's formula for the logarithmic derivative of the gamma function

2005-05-07

arxiv.org/abs/math/0505125v1

Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 120 (October 1996), no. 3, pp. 391--401. MR1388195 (97a:

Mathematics

Classical Analysis and ODEs

AMSTeX; Math Reviews MR #97a:11132

Scientific paper

We prove a remarkable formula of Ramanujan for the logarithmic derivative of the gamma function, which converges more rapidly than classical expansions, and which is stated without proof in Ramanujan's notebooks. The formula has a number of very interesting consequences which we derive, including an elegant hyperbolic summation, Ramanujan's formula for the Riemann zeta function evaluated at the odd positive integers, and new formulae for Euler's constant, gamma.

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