Difference between revisions of "Fresnel C"
From specialfunctionswiki
| Line 5: | Line 5: | ||
<gallery> | <gallery> | ||
File:Fresnelcplot.png| Graph of $C$. | File:Fresnelcplot.png| Graph of $C$. | ||
| − | File:Complexfresnelcplot.png|[[Domain coloring | + | File:Complexfresnelcplot.png|[[Domain coloring]] of Fresnel $C$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
Revision as of 22:47, 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.)
Graph of $C$.
Domain coloring 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)
