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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 6, Pages 365-375

On the sine integral and the convolution

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 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.


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.