Proof of a generalization of the (B.2) supercongruence of Van Hamme through a q-microscope

Abstract

We prove some q-congruences for certain truncated basic hypergeometric series by using Andrews' multiseries generalization of Watson's transformation and the creative microscoping method, recently devised by the author and Wadim Zudilin. As a conclusion, we completely confirm Conjecture 1.1 in Guo (2017) [10] which is a generalization of the (B.2) supercongruence of Van Hamme, and partially confirm Conjecture 4.3 in the same paper. We also raise several related conjectures on q-congruences.