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 | ||
| − | $$C(z)=\int_0^z \cos(t^2) \mathrm{d}t.$$ | + | $$C(z)=\int_0^z \cos\left(t^2\right) \mathrm{d}t.$$ |
(Note in Abramowitz&Stegun it [http://specialfunctionswiki.org/mirror/abramowitz_and_stegun-1.03/page_300.htm is defined] differently.) | (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"> | ||
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)
