Fresnel C

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

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

Cosine integral

Cosh integral

Exp integral $E_n$

Exp integral $\mathrm{Ei}$

Fresnel $C$

Fresnel $S$

Gudermannian

Inverse $\mathrm{gd}$

Sine integral

Log integral

Sinh integral