International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 37, Pages 2327-2333
doi:10.1155/S0161171203211510

On the Fresnel sine integral and the convolution

Adem Kılıçman

Department of Mathematics and Institute of Advanced Technology (ITMA) and Mathematical Research Institute (INSPEM), University Putra Malaysia, Serdang UPM 43400, Selangor, Malaysia

Received 19 November 2002; Revised 7 March 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.