Difference between revisions of "Fresnel C"
From specialfunctionswiki
| (11 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
The Fresnel C function is defined by the formula | The Fresnel C function is defined by the formula | ||
| − | $$C( | + | $$C(z)=\int_0^z \cos\left(t^2\right) \mathrm{d}t.$$ |
| − | (Note in Abramowitz&Stegun it [http:// | + | (Note in Abramowitz&Stegun it [http://specialfunctionswiki.org/mirror/abramowitz_and_stegun-1.03/page_300.htm is defined] differently.) |
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Fresnelcplot.png| Graph of $C$. |
| − | File: | + | File:Complexfresnelcplot.png|[[Domain coloring]] of Fresnel $C$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
=Properties= | =Properties= | ||
| − | < | + | [[Fresnel C is odd]]<br /> |
| − | + | [[Taylor series for Fresnel C]]<br /> | |
| − | + | [[Fresnel C in terms of erf]]<br /> | |
| − | + | [[Limiting value of Fresnel C]]<br /> | |
| − | |||
| − | </ | ||
| − | </ | ||
=See Also= | =See Also= | ||
| Line 22: | Line 19: | ||
=Videos= | =Videos= | ||
| − | [https://www.youtube.com/watch?v=fR4yd6pB5co How to integrate cos(x^2) - The Fresnel Integral C(x)]<br /> | + | [https://www.youtube.com/watch?v=fR4yd6pB5co How to integrate cos(x^2) - The Fresnel Integral C(x) (2 December 2014)]<br /> |
| + | [https://www.youtube.com/watch?v=H3uOq7VujYA Math and Physics: The Fresnel Integrals (12 May 2016)] <br /> | ||
| + | |||
| + | {{:*-integral functions footer}} | ||
| − | + | [[Category:SpecialFunction]] | |
Latest revision as of 05:10, 21 December 2017
The Fresnel C function is defined by the formula $$C(z)=\int_0^z \cos\left(t^2\right) \mathrm{d}t.$$ (Note in Abramowitz&Stegun it is defined differently.)
Graph of $C$.
Domain coloring of Fresnel $C$.
Properties
Fresnel C is odd
Taylor series for Fresnel C
Fresnel C in terms of erf
Limiting value of Fresnel C
See Also
Videos
How to integrate cos(x^2) - The Fresnel Integral C(x) (2 December 2014)
Math and Physics: The Fresnel Integrals (12 May 2016)
