Difference between revisions of "Fresnel C"
From specialfunctionswiki
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The Fresnel C function is defined by the formula | The Fresnel C function is defined by the formula | ||
$$C(x)=\int_0^x \cos(t^2) dt.$$ | $$C(x)=\int_0^x \cos(t^2) dt.$$ | ||
| − | + | (Note in Abramowitz&Stegun it [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/page_300.htm is defined] differently.) | |
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
Revision as of 10:31, 30 December 2015
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.)
- Fresnel.png
Fresnel integrals on $\mathbb{R}$.
Domain coloring of analytic continuation of Fresnel $C$.
Properties
Theorem: The following limit is known: $$\displaystyle\lim_{x \rightarrow \infty} C(x) = \displaystyle\int_0^{\infty} \cos(t^2)dt = \sqrt{ \dfrac{\pi}{8}}.$$
Proof: █
See Also
Videos
How to integrate cos(x^2) - The Fresnel Integral C(x)
