International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 3, Pages 517-524
doi:10.1155/S0161171291000704

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

O. Yürekli1 and I. Sadek2

 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

Abstract

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.