Supercongruences for a truncated hypergeometric series

preprint2011arXivOpen access

Abstract

The purpose of this note is to obtain some congruences modulo a power of a prime pp involving the truncated hypergeometric series ∑k=1p−1(x)k(1−x)k(1)k2⋅1ka\sum_{k=1}^{p-1} {(x)_k(1-x)_k\over (1)_k^2}\cdot{1\over k^a} for a=1a=1 and a=2a=2. In the last section, the special case x=1/2x=1/2 is considered.

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