Re: Inverse Laplace Transform

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• Subject: [mg131996] Re: Inverse Laplace Transform
• From: bakerbakura at gmail.com
• Date: Tue, 12 Nov 2013 00:17:10 -0500 (EST)
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```On Wednesday, 7 April 2010 13:26:49 UTC+2, Leslaw Bieniasz  wrote:
> Hi,
>
> I need to find an inverse Laplace transform of the
> expression:
>
> Sqrt[s*(s+a)]/(s-b)
>
> where "s" is the Laplace variable, "a" is a real positive constant,
> and "b" is a real constant that can be either positive or negative.
> I have tried the InverseLaplaceTransform[] function, but it
> returns the original expression. My question is: does this mean
> that the inverse transform does not exist, or only Mathematica
> cannot find it?
> Also, if anybody knows where I could possibly find the inverse
> in any book, or how I might obtain the inverse otherwise, I would
> appreciate an information. Abramowitz and Stegun book does not have it.
>
> Leslaw

Hi Leslaw

It's probably the case that the function does have an inverse Laplace transform, but that Mathematica cannot find it because it does not have a nice closed form in terms of elementary or special functions. You can probably invert it numerically if that is all you need.

Liam

P.S. Right now I'm actually having the opposite problem - Mathematica tells me that the Laplace transform of s particular function is something, but I have no idea how it proved it...

```

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