A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4)

Abstract

Long and Ramakrishna [Some supercongruences occurring in truncated hyper- geometric series, Adv. Math. 290 (2016) 773–808] generalized the (H.2) supercongruence of Van Hamme to the modulus [Formula: see text] case. In this paper, we give a [Formula: see text]-analogue of Long and Ramakrishna’s result for [Formula: see text]. A [Formula: see text]-congruence modulo the fourth power of a cyclotomic polynomial, which is a deeper [Formula: see text]-analogue of the (A.2) supercongruence of Van Hamme for [Formula: see text], is also formulated.

Topics & Concepts