A p-adic analogue of a formula of Ramanujan

Details A p-adic analogue of a formula of Ramanujan A p-adic analogue of a formula of Ramanujan

2007-08-24

arxiv.org/abs/0708.3307v1

Archiv der Mathematik 91 (2008), 492-504

Mathematics

Number Theory

10 pages

Scientific paper

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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