Power Series Expansion for Exponential Integral Function plus Logarithm

Theorem

 * $\ds \map \Ei x = -\gamma - \ln x + \sum_{n \mathop = 1}^\infty \paren {-1}^{n + 1} \frac {x^n} {n \times n!}$

where:
 * $\Ei$ denotes the exponential integral function
 * $\gamma$ denotes the Euler-Mascheroni constant
 * $x$ is a real number with $x > 0$.