LAUSR

Abstract 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 = 0 n ( 6 k + 1 ) ( 2 k k ) 3 ( − 512 ) n − k ≡ 0 ( mod 4 ( 2 n + 1 ) ( 2 n n ) ) , 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.