Hypergeometric evaluation identities and supercongruences

Ling Long

Vol. 249 (2011), No. 2, 405–418

DOI: 10.2140/pjm.2011.249.405

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