q-analogues of the G.2 Supercongruence of Van Hamme

Abstract

Motivated by the recent research of congruences and q-congruences, we provide two different q-analogues of the (G.2) supercongruence of Van Hamme through the 'creative microscoping' method, which was devised by Guo and Zudilin. It is a remarkable fact that this is the first time to give direct q-analogues of (G.2). In addition, we propose a conjecture related to Swisher's Dwork-type supercongruence (G.3).

Some supercongruences arising from symbolic summation

“…In 2015, Swisher proved this supercongruence (1.6). Not long ago, the authors [19] reproved it by giving the following q-analogue:…”