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

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dc.creatorBradley, David M.
dc.date2005-05-07
dc.date.accessioned2026-07-07T08:06:53Z
dc.date.available2026-07-07T08:06:53Z
dc.descriptionWe 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.
dc.descriptionAMSTeX; Math Reviews MR #97a:11132
dc.identifierhttps://arxiv.org/abs/math/0505125
dc.identifierhttp://arxiv.org/abs/math/0505125
dc.identifierMathematical Proceedings of the Cambridge Philosophical Society, Vol. 120 (October 1996), no. 3, pp. 391--401. MR1388195 (97a:11132)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130759
dc.subjectClassical Analysis and ODEs
dc.subjectNumber Theory
dc.subject33B15 (Primary), 11Y60 (Secondary)
dc.titleRamanujan's formula for the logarithmic derivative of the gamma function
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