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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
AMSTeX; Math Reviews MR #97a:11132

Keywords

Classical Analysis and ODEs, Number Theory, 33B15 (Primary), 11Y60 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/130759

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505125
 http://arxiv.org/abs/math/0505125
 Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 120 (October 1996), no. 3, pp. 391--401. MR1388195 (97a:11132)

Collections

arXiv