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

TL;DR

This paper generalizes recent results connecting partition functions related to Ramanujan's mock theta functions, providing new identities and reproofs of known theorems, thereby deepening understanding of mock theta functions and their combinatorial interpretations.

Contribution

The paper introduces two-variable generalizations of existing identities involving partition functions linked to mock theta functions, offering new proofs and insights.

Findings

Generalized identities for $p_{\omega}(n)$ and $p_{ u}(n)$

Reproved results analogous to Euler's pentagonal number theorem

Enhanced understanding of mock theta functions' combinatorial properties

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.