Fresnel Integrals

Fresnel Integrals S(x) and C(x) are two transcendal functions named after
Augustin-Jean Fresnel that are used in Optics and are closely related to the
error function (erf). They arise in the description of [[near-field Fresnel
diffraction]] phenomena and are defined through the following integral
representations:

S(x) = I(sin(t^2)dt):0-x, C(x) = I(cos(t^2)dt):0-x

The simultaneous parametric plot of S(x) and C(x) is the Euler Spiral

Transcendal Function