New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences

Abstract

In terms of a very-well-poised 6 ϕ 5 summation formula, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we establish four new q-supercongruences for truncated basic hypergeometric series. One of these results is a new q-analogue of the (F.2) supercongruence of Van Hamme.