“Divergent” Ramanujan-type supercongruences

Guillera, Jesús; Zudilin, Wadim

doi:10.1090/S0002-9939-2011-10950-X

“Divergent” Ramanujan-type supercongruences
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by Jesús Guillera and Wadim Zudilin PDF

Proc. Amer. Math. Soc. 140 (2012), 765-777 Request permission

Abstract:

“Divergent” Ramanujan-type series for $1/\pi$ and $1/\pi ^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases. In this paper we manage to prove three of the supercongruences by means of the Wilf–Zeilberger algorithmic technique.

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