What is "q-exponential"

In combinatorial mathematics, a q-exponential is a q-analog of the exponential function, namely the eigenfunction of a q-derivative. There are many q-derivatives, for example, the classical q-derivative, the Askey-Wilson operator, etc. Therefore, unlike the classical exponentials, q-exponentials are not unique. For example, e(z) is the q-exponential corresponding to the classical q-derivative while E(z) are eigenfunctions of the Askey-Wilson operators.