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arXiv · 0708.3307

A p-adic analogue of a formula of Ramanujan

Dermot McCarthy·Robert Osburn
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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.

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Dermot McCarthy, Robert Osburn. 2007-08-24. A p-adic analogue of a formula of Ramanujan. https://doi.org/10.1007/s00013-008-2828-0

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