Ramanujan-type formulae for 1/π: the art of translation
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🧮 math.NT
math.CA
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hypergeometricidentitiesramanujan-typealgebraicanalysisarithmeticasymptoticcomputed
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We outline an elementary method for proving numerical hypergeometric identities, in particular, Ramanujan-type identities for $1/\pi$. 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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