In this paper we consider an example of a Maass waveform which was
constructed by Cohen from a function $\sigma$, studied by Andrews, Dyson and
Hickerson, and it's companion $\sigma^*$. We put this example in a more general
framework.
In this paper we consider level l Appell functions, and find a partial
differential equation for all odd l. For l=3 this recovers the Rank-Crank PDE,
found by Atkin and Garvan, and for l=5 we get a similar PDE found by Garvan.