On the (K.2) supercongruence of Van Hamme

Osburn, Robert; Zudilin, Wadim

doi:10.1016/j.jmaa.2015.08.009

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On the (K.2) supercongruence of Van Hamme

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Osburn, Robert
Max Planck Institute for Mathematics, Max Planck Society;

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Zudilin, Wadim
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.1016/j.jmaa.2015.08.009
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arXiv:1504.01976.pdf
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Osburn, R., & Zudilin, W. (2016). On the (K.2) supercongruence of Van Hamme. Journal of Mathematical Analysis and Applications, 433(1), 706-711. doi:10.1016/j.jmaa.2015.08.009.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6ADF-B

Abstract

We prove the last remaining case of the original 13 Ramanujan-type supercongruence conjectures due to Van Hamme from 1997. The proof utilizes classical congruences and a WZ pair due to Guillera. Additionally, we mention some future directions concerning this type of supercongruence.