Universal mock theta functions and two-variable Hecke–Rogers identities

Abstract

We obtain two-variable Hecke–Rogers identities for three universal mock theta functions. This implies thatmany of Ramanujan’smock theta functions, including all the third-order functions, have aHecke–Rogers-type double sumrepresentation. We find new generating function identities for the Dyson rank function, the overpartition rank function, the M2-rank function and related spt-crank functions. Results are proved using the theory of basic hypergeometric functions.