Some Identities associated with mock theta functions $\omega (q)$ and $\nu (q)$

Abstract

Recently, Andrews, Dixit and Yee defined two partition functions $p_{\omega }(n)$ and $p_{\nu }(n)$ that are related with Ramanujan's mock theta functions $\omega (q)$ and $\nu (q)$, respectively. In this paper, we present two variable generalizations of their results. As an application, we reprove their results on $p_{\omega }(n)$ and $p_{\nu }(n)$ that are analogous to Euler's pentagonal number theorem.