Difference between revisions of "Fresnel C"

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(Properties)
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File:Complexfresnelcplot.png|[[Domain coloring]] of Fresnel $C$.
 
File:Complexfresnelcplot.png|[[Domain coloring]] of Fresnel $C$.
 
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=Properties=
 
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<strong>Theorem:</strong> The following limit is known:
 
$$\displaystyle\lim_{x \rightarrow \infty} C(x) = \displaystyle\int_0^{\infty} \cos(t^2)dt = \sqrt{ \dfrac{\pi}{8}}.$$
 
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<strong>Proof:</strong> █
 
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Revision as of 22:48, 23 May 2016

The Fresnel C function is defined by the formula $$C(x)=\int_0^x \cos(t^2) dt.$$ (Note in Abramowitz&Stegun it is defined differently.)

See Also

Fresnel S

Videos

How to integrate cos(x^2) - The Fresnel Integral C(x)

<center>$\ast$-integral functions
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