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When is Laplace transform of a function power-law and relation to the behavior of the functi...

I want to see when the Laplace transform of a non-negative function $f$ defined on $[0, +\infty)$ is a power function in the loose sense, i.e., $$g(s) = \mathcal L\{f\}(x) = \int_0^\infty f(x) e^{-sx} …
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