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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 41, Pages 2635-2643

On the Fresnel integrals and the convolution

1Department of Mathematics, University of Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
2Institute of Advanced Technology, University of Putra Malaysia, Serdang, Selangor 43400 UPM, Malaysia
3Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK

Received 24 November 2002

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.


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 xr are evaluated.