Ramanujan-type formulae for 1/π1/π: the art of translation

preprint2013arXivOpen access

Abstract

We outline an elementary method for proving numerical hypergeometric identities, in particular, Ramanujan-type identities for 1/π1/π. The principal idea is using algebraic transformations of arithmetic hypergeometric series to translate non-singular points into singular ones, where the required constants can be computed using asymptotic analysis.

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