Difference between revisions of "Fresnel S"
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File:Fresnelsplot.png| Graph of $S$. | File:Fresnelsplot.png| Graph of $S$. | ||
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Revision as of 22:41, 23 May 2016
The Fresnel $S$ function is defined by $$S(z)=\int_0^z \sin(t^2) dt.$$ (Note in Abramowitz&Stegun it is defined differently.)
Graph of $S$.
Domain coloring of analytic continuation of Fresnel $S$.
Properties
Theorem: The following limit is known: $$\displaystyle\lim_{x \rightarrow \infty} S(x) = \displaystyle\int_0^{\infty} \sin(t^2)dt = \sqrt{ \dfrac{\pi}{8}}.$$
Proof: █
See Also
Videos
The Fresnel Integral S(x) - How to integrate sin(x^2)
