Congruences for generalized Apéry numbers and Gaussian hypergeometric series

For positive integers f1, f2, m, l, we define a generalization of Apéry numbers A(f1, f2, m, l, λ) given by A(f1,f2,m,l,λ):=∑j=0f2(f1+jj)m(f2j)lλj.In this article, we deduce congruence relations satisfied by these generalized Apéry numbers extending results of (Coster in Supercongruences, Ph.D. thesis, Universiteit Leiden, 1988). We find expressions of A(f1, f2, m, l, λ) in terms of Gaussian hypergeometric series and evaluate some new supercongruences similar to Beukers’ supercongruences. © 2017, The Author(s).