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SUPERCONGRUENCES INVOLVING $p$ -ADIC GAMMA FUNCTIONS

  • JI-CAI LIU (a1)

Abstract

We establish some supercongruences for the truncated $_{2}F_{1}$ and $_{3}F_{2}$ hypergeometric series involving the $p$ -adic gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated $_{3}F_{2}$ hypergeometric series. Related supercongruences modulo $p^{3}$ are proposed as conjectures.

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SUPERCONGRUENCES INVOLVING $p$ -ADIC GAMMA FUNCTIONS

  • JI-CAI LIU (a1)

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