q-analogues of the (G.2) supercongruence of Van Hamme
Yudong Liu, Xiaoxia Wang
Abstract
Motivated by the recent research of congruences and q-congruences, we provide two different q-analogues of the (G.2) supercongruence of Van Hamme through the “creative microscoping” method, which was recently devised by Guo and Zudilin. It is a remarkable fact that this is the first time giving q-analogues of (G.2). In addition, we propose a conjecture on a partial q-analogue of Swisher’s Dwork-type supercongruence (G.3).
Topics & Concepts
Congruence relationMathematicsConjectureCombinatoricsType (biology)Pure mathematicsDiscrete mathematicsAlgebra over a fieldEcologyBiologyAdvanced Mathematical IdentitiesAnalytic Number Theory ResearchMathematical functions and polynomials