Multidimensional transform: Difference between revisions

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== Multidimensional Laplace transform ==

The multidimensional Laplace transform is useful for the solution of boundary value problems. Boundary value problems in two or more variables characterized by partial differential equations can be solved by a direct use of the Laplace transform.<ref name=":0">{{Cite journal|title = Theorems on multidimensional laplace transform for solution of boundary value problems|journal = Computers & Mathematics with Applications|date = 1989-01-01|pages = 1033–1056|volume = 18|issue = 12|doi = 10.1016/0898-1221(89)90031-X|first = Joyati|last = Debnath|first2 = R. S.|last2 = Dahiya|doi-access = free}}</ref> The Laplace transform for an M-dimensional case is defined<ref name=":0"/> as

<math> F(s_1,s_2,\ldots,s_n) = \int_{0}^{\infty} \cdots \int_{0}^{\infty}