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CONGRUENCES FOR TRUNCATED HYPERGEOMETRIC SERIES $_{2}F_{1}$

Published online by Cambridge University Press:  06 March 2017

JI-CAI LIU*
Affiliation:
College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, PR China email [email protected]
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Abstract

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Rodriguez-Villegas conjectured four supercongruences associated to certain elliptic curves, which were first confirmed by Mortenson by using the Gross–Koblitz formula. In this paper we prove four supercongruences between two truncated hypergeometric series $_{2}F_{1}$. The results generalise the four Rodriguez-Villegas supercongruences.

Type
Research Article
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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