Supercongruences for a truncated hypergeometric series

Details Supercongruences for a truncated hypergeometric series Supercongruences for a truncated hypergeometric series

2010-07-22

arxiv.org/abs/1007.3852v2

Mathematics

Number Theory

Revised version

Scientific paper

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

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