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version). This leads to difference in the way you evalutate the Mellin integral. For example, the one-sided transform has an implicit step function in time-domain which corresponds to evaluating the Mellin integral by encirceling the poles in some left half plane and using Cauchy's residue theorem. Perhaps one can add a paragraph about inversion to the two-sided
Laplace transform page, but at the moment I have no time.
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The section on the properties of the two-sided
Laplace transform is wrong. Also, there is no reference as to who invented it. It is not an old invention, it was invented by 3 Japanese engineers in 1999. A proposal for two-sided Laplace transforms and its application to electronic circuitsOriginal
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The inverse of the two-sided
Laplace transform is given by the Mellin integral inside the region of convergence, just like in the one-sided case. The main difference is the location of possible poles in s-space (there are no poles to the right of some suitable vertical line for the one-sided
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Research
Article Applied Mathematics and Computation, Volume 100, Issue 1, April 1999, Pages 1-11. Isamu Matsuzuka, Koji Nagasawa, Akihiro Kitahama
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Knowledge. If you would like to participate, please visit the project page, where you can join
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Is there a formula for the inverse of two-sided
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the formula for the inverse of one-sided
Laplace transform
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What does the comment "does not respect causality" mean?
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