Radial limits of the universal mock theta function 𝑔₃

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 g_2 and g 3 g_3 . Recently, Bringmann and Rolen found such formulas for specializations of g 2 g_2 . Here we treat the case of g 3 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.