Multidimensional transform: Difference between revisions

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A special case (along 2 dimensions) of the multi-dimensional Laplace transform of function f(x,y) is defined<ref>{{Cite book|title = Operational Calculus in two Variables and its Application (1st English edition) - translated by D.M.G. Wishart (Calcul opérationnel)|last = |first = |publisher = |year = |isbn = |___location = |pages = }}</ref> as

<math display="block">F(s_1,s_2)=\textstyle \int\limits_{0}^{\infty}\int\limits_{0}^{\infty}\ f(x,y) e^{-s_1x-s_2y}\, dxdy</math>

<math> F(s_1,s_2) </math> is called the image of <math> f(x,y) </math> and <math> f(x,y) </math> is known as the original of <math> F(s_1,s_2) </math>.<ref name=":1">{{Cite journal|url = |title = Multi-Dimensional Laplace Transforms and Systems of Partial Differential Equations |last = Aghili and Moghaddam|journal = International Mathematical Forum |volume=1 |year=2006 |issue=21 |pages=1043–1050|doi = 10.12988/imf.2006.06084|pmid = |access-date = }}</ref> This special case can be used to solve the [[Telegrapher's equations]].<ref name=":1" />