Radial Limits of the Universal Mock Theta Function $g_3$

Understand

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.