International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 6, Pages 365-375
doi:10.1155/S0161171202007834

On the sine integral and the convolution

Brian Fisher1,2 and Fatma Al-Sirehy3

1Department of Mathematics and Computer Sciences, Leicester University, Leicester LE1 7RH, UK
2Department of Mathematical Sciences, Faculty of Computer Sciences and Engineering, De Montfort University, The Gateway, Leicester LE1 9BH, UK
3King Abdulaziz University, P.O. Box 32477, Jeddah, Saudi Arabia

Received 7 June 2001

Copyright © 2002 Brian Fisher and Fatma Al-Sirehy. 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 sine integral Si(λx) and the cosine integral Ci(λx) and their associated functions Si+(λx), Si−(λx), Ci+(λx), Ci−(λx) are defined as locally summable functions on the real line. Some convolutions of these functions and sin(μx), sin+(μx), and sin−(μx) are found.