Difference between revisions of "Fresnel C"

From specialfunctionswiki
Jump to: navigation, search
 
(One intermediate revision 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
$$C(x)=\int_0^x \cos(t^2) \mathrm{d}t.$$
+
$$C(z)=\int_0^z \cos\left(t^2\right) \mathrm{d}t.$$
 
(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.)

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