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

computational resources

• https://docs.google.com/file/d/0B8XXo8Tve1cxbG1sMTgwX1A4MEk/edit