A p-adic analogue of a formula of Ramanujan
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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 series supercongruences
Mathematics Subject Classification (2000).Primary 33C20 Secondary 11S80
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