Multi-dimensional Laplace transforms and applications
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In this dissertation we establish new theorems for computing certain types of multidimensional Laplace transform pairs from known one-dimensional Laplace transforms. The theorems are applied to the most commonly used special functions and so we obtain many two and three dimensional Laplace transform pairs. As applications, some boundary-value problems involving linear partial differential equations are solved by the use of multi-dimensional Laplace transformation. Also we establish some relations between the Laplace transformation and other integral transformations in two variables.