Fresnel integral

The formula defines the Fresnel cosine integral C(x) and the Fresnel sine integral S(x):

  

Most authors use a term p t² / 2 instead of t² in the integral, resulting in a values 2/p times as large.

The Fresnel integral has important applications in the physics of diffraction and is used in the theory of driving motorcar round a corner quickly.

The curve can be expanded in terms of the spherical Bessel function of the first kind.