Next to leading order QED corrections to the process $\gamma \gamma \to {\mu }^{+}{\mu }^{-}\gamma$

We have calculated one loop quantum electrodynamic corrections to the process $\gamma \gamma \to {\mu }^{+}{\mu }^{-}\gamma$, where all photons are on mass shell and the muon mass is taken into account. The result is obtained in the analytical form and is implemented as functions in the C programming language, which can be used to calculate the cross-section, the differential cross section, and to construct generators. We also present numerical results for corrections to the cross section and to the differential cross section.