Taylor series for Fresnel S
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Revision as of 17:14, 5 October 2016 by Tom (talk | contribs) (Created page with "==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...")
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.
