International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 2, Pages 363-376

Theorems on association of variables in multidimensional Laplace transforms

Joyati Debnath and Narayan Chandra Debnath

Department of Mathematics and Computer Science, University of Wisconsin, River Falls, River Falls 54022, Wisconsin, USA

Received 1 May 1988; Revised 2 December 1988

Copyright © 1989 Joyati Debnath and Narayan Chandra Debnath. 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 inverse of the multidimensional Laplace transform is often obtained by the method of association of variables. In this paper, some basic theorems are developed for evaluating the associated transform of certain types of transformed functions. Many useful associated pairs can be produced with the aid of these fundamental theorems. Several illustrative examples are included.