Difference between revisions of "Fresnel S in terms of erf"
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(Created page with "==Theorem== The following formula holds: $$S(z)=\sqrt{\dfrac{\pi}{2}} \dfrac{1+i}{4} \left[ \mathrm{erf} \left( \dfrac{1+i}{\sqrt{2}} z \right) - i \mathrm{erf} \left( \dfrac{...") |
m (Tom moved page Fresnel S in terms of error function to Fresnel S in terms of erf) |
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Latest revision as of 17:17, 5 October 2016
Theorem
The following formula holds: $$S(z)=\sqrt{\dfrac{\pi}{2}} \dfrac{1+i}{4} \left[ \mathrm{erf} \left( \dfrac{1+i}{\sqrt{2}} z \right) - i \mathrm{erf} \left( \dfrac{1-i}{\sqrt{2}} z \right) \right],$$ where $S$ denotes Fresnel S, $\pi$ denotes pi, $i$ denotes the imaginary number, and $\mathrm{erf}$ denotes the error function.
