Andrews-Garvan crank modular form

introduction

$$ C(w;q)=\frac{(q)_{\infty}}{(wq;q)_{\infty}(w^{-1}q;q)_{\infty}} $$

• specialization $C(-1;q)=b(q)$ where

$$b(q)=q^{1/24}\frac{\eta(\tau)}{\eta(2\tau)}\theta(-q)$$

• see 3rd order mock theta functions

related items

• Dyson's rank generating function
• Quantum modular forms