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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

``Divergent'' Ramanujan-type supercongruences


Authors: Jesús Guillera and Wadim Zudilin
Journal: Proc. Amer. Math. Soc. 140 (2012), 765-777
MSC (2010): Primary 11Y55, 33C20, 33F10; Secondary 11B65, 11D88, 11F33, 11F85, 11S80, 12H25, 40G99, 65-05, 65B10
Published electronically: July 21, 2011
MathSciNet review: 2869062
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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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Additional Information

Jesús Guillera
Affiliation: Av. Cesáreo Alierta, 31 esc. izda 4$^{∘}$–A, Zaragoza, Spain
Email: jguillera@gmail.com

Wadim Zudilin
Affiliation: School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia
Email: wadim.zudilin@newcastle.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10950-X
PII: S 0002-9939(2011)10950-X
Keywords: Congruence, hypergeometric series, Ramanujan-type identities for $1/\pi$, creative telescoping
Received by editor(s): August 12, 2010
Received by editor(s) in revised form: December 14, 2010
Published electronically: July 21, 2011
Additional Notes: Work of the second author was supported by Australian Research Council grant DP110104419.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.