Vol. 249, No. 2, 2011

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Hypergeometric evaluation identities and supercongruences

Ling Long

Vol. 249 (2011), No. 2, 405–418
Abstract

We apply some hypergeometric evaluation identities, including a strange valuation of Gosper, to prove several supercongruences related to special valuations of truncated hypergeometric series. In particular, we prove a conjecture of van Hamme.

Keywords
Ramanujan supercongruences, hypergeometric identities
Mathematical Subject Classification 2000
Primary: 33C20
Milestones
Received: 1 December 2009
Revised: 27 September 2010
Accepted: 13 October 2010
Published: 1 February 2011
Authors
Ling Long
Department of Mathematics
Iowa State University
396 Carver Hall
Ames, IA 50011
United States
http://www.math.iastate.edu/linglong