Power Series Expansion for Fresnel Cosine Integral Function

Theorem

 * $\displaystyle \map {\operatorname C} x = \sqrt {\frac 2 \pi} \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {x^{4 n + 1} } {\paren {4 n + 1} \paren {2 n}!}$

where $\operatorname C$ denotes the Fresnel cosine integral function.