Power Series Expansion for Exponential Integral Function/Formulation 2

Theorem
Let $\Ei: \R_{>0} \to \R$ denote the exponential integral function:


 * $\map \Ei x = \ds \int_{t \mathop \to -\infty}^{t \mathop = x} \frac {e^t} t \rd t$

Then:

where $\gamma$ denotes the Euler-Mascheroni constant.