On the Fresnel integrals and the convolution (Q1415118)

Summary: The Fresnel cosine integral \(C(x)\), the Fresnel sine integral \(S(x)\), and the associated functions \(C_{+}(x)\), \(C_{-}(x)\), \(S_{+}(x)\), and \(S_{-}(x)\) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with \(x^{r}_{+}\) and \(x^r\) are evaluated.