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A p-adic analogue of a formula of Ramanujan

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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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Authors and Affiliations

  1. School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland

    Dermot McCarthy & Robert Osburn

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  1. Dermot McCarthy
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  2. Robert Osburn
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Correspondence to Dermot McCarthy.

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Received: 11 April 2008

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McCarthy, D., Osburn, R. A p-adic analogue of a formula of Ramanujan. Arch. Math. 91, 492–504 (2008). https://doi.org/10.1007/s00013-008-2828-0

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  • DOI: https://doi.org/10.1007/s00013-008-2828-0

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