Difference between revisions of "Fresnel C"

From specialfunctionswiki
Jump to: navigation, search
(Videos)
Line 18: Line 18:
  
 
=Videos=
 
=Videos=
[https://www.youtube.com/watch?v=fR4yd6pB5co How to integrate cos(x^2) - The Fresnel Integral C(x)]
+
[https://www.youtube.com/watch?v=fR4yd6pB5co How to integrate cos(x^2) - The Fresnel Integral C(x)]<br />
  
 
<center>{{:*-integral functions footer}}</center>
 
<center>{{:*-integral functions footer}}</center>

Revision as of 02:34, 4 June 2015

The Fresnel C function is defined by the formula $$C(x)=\int_0^x \cos(t^2) dt.$$

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:

Videos

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

<center>$\ast$-integral functions
</center>