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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 517-524

A Parseval-Goldstein type theorem on the widder potential transform and its applications

1Department of Mathematics and Computer Science, Ithaca College, Ithaca 14850, New York, USA
2Mathematical Sciences, University of North Carolina, Wilmington 28403, NC, USA

Received 19 March 1990; Revised 20 November 1990

Copyright © 1991 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.


In this paper a Parseval-Goldstein type theorem involving the Widder potential transform and a Laplace type integral transform is given. The theorem is then shown to yield a relationship between the 𝒦-transform and the Laplace type integral transform. The theorem yields some simple algorithms for evaluating infinite integrals. Using the theorem and its results, a number of new infinite integrals of elementary and special functions are presented. Some illustrative examples are also given.