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Rational Hypergeometric Ramanujan Identities for $1/\pi^c$: Survey and Generalizations

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arxiv 2101.12592 v1 pith:4F7SJT5R submitted 2021-01-29 math.NT

Henri Cohen , Jesús Guillera This is my paper · ORCID
classification math.NT
keywords hypergeometricidentitiesrationalgeneralizationsgiveprooframanujansurvey
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abstract

We give a simple unified proof for all existing rational hypergeometric Ramanujan identities for $1/\pi$, and give a complete survey (without proof) of several generalizations: rational hypergeometric identities for $1/\pi^c$, Taylor expansions, upside-down formulas, and supercongruences.

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Cited by 1 Pith paper

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  1. Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients

    math.NT 2025-09 conditional novelty 7.0 of 10

    New continued fractions yield the first proved reasonable irrationality measures for Chowla–Selberg gamma quotients, including μ(CS(-3)) < 5.548 and μ(CS(-163)) < 2.477.

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