Power Series Expansion for Cosine Integral Function plus Logarithm

Theorem

 * $\displaystyle \map \Ci x = -\gamma - \ln x + \sum_{n \mathop = 1}^\infty \paren {-1}^{n + 1} \frac {x^{2 n} } {\paren {2 n} \times \paren {2 n}!}$

where:
 * $\Ci$ denotes the cosine integral function
 * $\gamma$ denotes the Euler-Mascheroni constant
 * $x$ is a strictly positive real number.