Archiv der Mathematik

, Volume 91, Issue 6, pp 492–504

A p-adic analogue of a formula of Ramanujan

Article

DOI: 10.1007/s00013-008-2828-0

Cite this article as:
McCarthy, D. & Osburn, R. Arch. Math. (2008) 91: 492. doi:10.1007/s00013-008-2828-0

Abstract.

During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.

Keywords.

Gaussian hypergeometric seriessupercongruences

Mathematics Subject Classification (2000).

Primary 33C20Secondary 11S80

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity College DublinBelfield, Dublin 4Ireland