The formal solution of the radiative transfer equation can be expressed using exponential integrals. These are mathematical functions defined as:

\begin{equation}

E_n(x) = \int_1^{\infty}\, \exp (-yx)\frac{\mathrm{d}x}{y^n}, \;\;\;\;n = 1, 2, ...

\end{equation}

There is several important properties of these functions: