Equivalent functions for the Fresnel integral

Fresnel integral is modeled with three equivalent functions. The first function is derived by considering the sum of the first term of the Fresnel integral's asymptotic expansion {F(x)} and an exponential function which approaches to infinity at the zero of the Fresnel function's argument and has the properties of a unit step function. The second one is the sum of a unit step function and the transition function defined for the simplified uniform theory of diffraction. The third function considers directly eliminating the infinity coming from F(x). The amplitude and the phase of Fresnel integral and its equivalent functions are compared numerically. The result is applied to the modified theory of physical optics solution of the diffraction of edge waves from a half plane problem.