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Published in:
2019 | OriginalPaper | Chapter
Some Supercongruences for Truncated Hypergeometric Series
Authors : Ling Long, Ravi Ramakrishna
Published in: 2017 MATRIX Annals
Publisher: Springer International Publishing
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We prove various supercongruences involving truncated hypergeometric sums. These include a strengthened version of a conjecture of van Hamme. Our method is to employ various hypergeometric transformation and evaluation formulae to convert the truncated sums to quotients of Γ-values. We then convert these to quotients of Γ p-values and use Taylor’s Theorem to make p-adic approximations. In the cases under consideration higher order coefficients often vanish leading to the supercongruences.