Supercongruences satisfied by coefficients of \({}_2F_1\) hypergeometric series

Chan, Heng Huat and Kontogeorgis, Aristides and Krattenthaler, Christian and Osburn, Robert

Abstract

Recently, Chan, Cooper and Sica conjectured two congruences for coefficients of classical 2F1 hypergeometric series which also arise from power series expansions of modular forms in terms of modular functions. We prove these two congruences using combinatorial properties of the coefficients