A $p$-adic supercongruence for truncated hypergeometric series ${}_7F_6$

Ji-Cai Liu

doi:10.1007/s00025-017-0744-y

paper

A $p$ -adic supercongruence for truncated hypergeometric series $_{7} F_{6}$

arXiv:1611.10188 · doi:10.1007/s00025-017-0744-y

Abstract

Using an identity due to Gessel and Stanton and some properties of the $p$ -adic Gamma function, we establish a $p$ -adic supercongruence for truncated hypergeometric series $_{7} F_{6}$ . From it we deduce some related supercongruences, which extend certain recent results and confirm a supercongruence conjecture.

Results Math., online, 9 pages

A p-adic supercongruence for truncated hypergeometric series 7​F6​

Abstract

A $p$ -adic supercongruence for truncated hypergeometric series $_{7} F_{6}$