A q-analogue of the (A.2) supercongruence of Van Hamme for primes $$p\equiv 1\pmod {4}$$

Abstract

Recently, Wang and Yue gave a q-analogue of the (A.2) supercongruence of Van Hamme for any prime $$p\equiv 3\pmod {4}$$ by using a q-analogue of Watson’s $$_3F_2$$ summation and the creative microscoping method, devised by the author and Zudilin. In this note, we give the corresponding q-analogue of the (A.2) supercongruence of Van Hamme for all primes $$p\equiv 1\pmod {4}$$ in the same manner. A supercongruence conjecture similar to the (A.3) conjecture of Swisher is also presented.