Andrews, George E.George E.AndrewsDixit, AtulAtulDixitSchultz, DanielDanielSchultzYee, Ae JaAe JaYee2025-08-282025-08-282016-03-01https://d8.irins.org/handle/IITG2025/20019It was recently shown that q?(q), where ?(q) is one of the third order mock theta functions, is the generating function of p?(n), the number of partitions of a positive integer n such that all odd parts are less than twice the smallest part. In this paper, we study the overpartition analogue of p?(n), and express its generating function in terms of a 3?2 basic hypergeometric series and an infinite series involving little q-Jacobi polynomials. This is accomplished by obtaining a new seven parameter q-series identity which generalizes a deep identity due to the first author as well as its generalization by R.P.~Agarwal. We also derive two interesting congruences satisfied by the overpartition analogue, and some congruences satisfied by the associated smallest parts function.en-USNumber TheoryTheta functionAnaloguePolynomialse-Printe-Print123456789/555