A q-analogue of the (L.2) supercongruence of Van Hamme

The (L.2) supercongruence of Van Hamme was proved by Swisher recently. In this paper we provide a conjectural q-analogue of the (L.2) supercongruence of Van Hamme and prove a weaker form of it by using the q-WZ method. In the same way, we prove a complete q-analogue of the following congruence∑k=0n(6k+1)(2kk)3(−512)n−k≡0(mod4(2n+1)(2nn)), which was conjectured by Z.-W. Sun and confirmed by B. He. We also provide a conjectural q-analogue of another congruence proved by Swisher.