Fresnel Integral

Integrals of the form

are called Fresnel integrals. They were introduced by A. J. Fresnel for the solution of problems of the diffraction of light. In the case of improper Fresnel integrals, we have S(∞) = C(∞) = ½. Tables of Fresnel integrals are given in many handbooks (for example, E. Jahnke, F. Emde, and F. Lösch, Spetsial’nye funktsii, 2nd ed., 1968 [translated from German]).