A p-adic analogue of a formula of Ramanujan

Dermot McCarthy, Robert Osburn

Published 2007-08-24Version 1

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.