Difference between revisions of "Fresnel C"

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The Fresnel C function is defined by the formula
 
The Fresnel C function is defined by the formula
$$C(x)=\int_0^x \cos(t^2) dt.$$
+
$$C(z)=\int_0^z \cos\left(t^2\right) \mathrm{d}t.$$
(Note in Abramowitz&Stegun it [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/page_300.htm is defined] differently.)
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(Note in Abramowitz&Stegun it [http://specialfunctionswiki.org/mirror/abramowitz_and_stegun-1.03/page_300.htm is defined] differently.)
 
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=Properties=
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[[Fresnel C is odd]]<br />
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[[Taylor series for Fresnel C]]<br />
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[[Fresnel C in terms of erf]]<br />
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[[Limiting value of Fresnel C]]<br />
  
 
=See Also=
 
=See Also=
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=Videos=
 
=Videos=
[https://www.youtube.com/watch?v=fR4yd6pB5co How to integrate cos(x^2) - The Fresnel Integral C(x)]<br />
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[https://www.youtube.com/watch?v=fR4yd6pB5co How to integrate cos(x^2) - The Fresnel Integral C(x) (2 December 2014)]<br />
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[https://www.youtube.com/watch?v=H3uOq7VujYA Math and Physics: The Fresnel Integrals (12 May 2016)] <br />
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[[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.)

Properties

Fresnel C is odd
Taylor series for Fresnel C
Fresnel C in terms of erf
Limiting value of Fresnel C

See Also

Fresnel S

Videos

How to integrate cos(x^2) - The Fresnel Integral C(x) (2 December 2014)
Math and Physics: The Fresnel Integrals (12 May 2016)

$\ast$-integral functions