On the Fresnel sine integral and the convolution

Abstract

The Fresnel sine integral S(x), the Fresnel cosine integral C(x), and the associated functions S+(x), S−(x), C+(x), and C−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions with x+r, xr are evaluated.