Ecology

Pure mathematics

Biology

Type (biology)

Ramanujan's sum

Mathematics

Combinatorics

Journal of Mathematical Analysis and Applications

In this paper, we establish a new q-congruence with parameters modulo the fourth power of a cyclotomic polynomial from Watson's ϕ78 transformation. Taking parameters substitution in our new q-congruence, we present a q-analogue of the (D.2) supercongruence of Van Hamme and several different q-analogues of He's supercongruence for p≡1(mod3). Finally, we propose a Dwork-type supercongruence conjecture on He's supercongruence.

q-Analogues of two Ramanujan-type supercongruences