Radial Limits of the Universal Mock Theta Function $g_3$

TL;DR

This paper investigates the radial limits of the universal mock theta function g_3, providing explicit formulas and generalizations that extend previous results for related mock theta functions and rank generating functions.

Contribution

It derives explicit formulas for the radial limits of g_3, generalizing prior results and offering new expressions for fifth order mock theta functions.

Findings

Explicit formulas for g_3 radial limits

Generalization of rank generating function limits

New expressions for fifth order mock theta functions

Abstract

Referring to Ramanujan's original definition of a mock theta function, Rhoades asked for explicit formulas for radial limits of the universal mock theta functions $g_2$ and $g_3$. Recently, Bringmann and Rolen found such formulas for specializations of $g_2$. Here we treat the case of $g_3$, generalizing radial limit results for the rank generating function of Folsom, Ono, and Rhoades. Furthermore, we find expressions for radial limits of fifth order mock theta functions different from those of Bajpai, Kimport, Liang, Ma, and Ricci.