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).