Taylor series for Fresnel S
From specialfunctionswiki
Theorem
The following Taylor series holds: $$S(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k x^{4k+3}}{(2k+1)!(4k+3)},$$ where $S$ denotes Fresnel S and $(2k+1)!$ denotes the factorial.
