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How can I prove that in formal way, this function doesn't have inverse Laplace transform. $$ F(s)=\frac{\sin(s)}{\sqrt{s}} $$ Strictly it should be in Bromwich contour method. Could you please tell ...

I would like to ask the following two: For the integral: \begin{equation} \int_{0}^{t}\left( 1-s^p \right)^{\frac{1-p}{p}}ds \end{equation} I know that it is reduced to the following product ...

Problem I asked a question at Math.SE last year and later offered a bounty for it, but it remains unsolved even in the simplest case. So I finally decided to repost this case here, (I know the ...