On weighted overpartitions related to some q-series in Ramanujan’s lost notebook

Abstract

Motivated by certain [Formula: see text]-series of Ramanujan, we examine two overpartition difference functions. We give both combinatorial and asymptotic formulas for the differences and show that they are always positive. We also briefly discuss similar differences for some other types of partitions. Our main tools are elementary [Formula: see text]-series transformations and Ingham’s Tauberian theorem.