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

Bradley, David M. (1996) Ramanujan's formula for the logarithmic derivative of the gamma function. [Preprint]

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      Abstract

      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 the notebooks \cite5. 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, $\g$.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Subjects: 33-xx Special functions > 33Bxx Elementary classical functions
      11-xx Number theory > 11Yxx Computational number theory
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 24 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/153

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