The Graphs of Quantum Dilogarithm

Using the complex coloring method, we present the graphs of the quantum dilogarithm function $G_b(z)$ and visualize its analytic and asymptotic behaviours. In particular we demonstrate the limiting process when the modified $G_b(z)\to \mathrm{\Gamma }(z)$ as $b\to 0$. We also survey the relations of $G_b(z)$ with different variants of the quantum dilogarithm function.