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I am trying to find the inverse Laplace transform of the Gaussian function $$ G(s)=e^{-cs^2}$$

$L^{-1}\left\{G(s)\right\}= ?$ Where $c> 0$.

Matti P.
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saido saido
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match [many users' quality standards](http://goo.gl/mLWc8), so it may attract downvotes, or be put on hold. To prevent that, please [edit] the question. [This](http://goo.gl/PlJyVQ) will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Aug 26 '19 at 10:11
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    You mean $c < 0$ then its bilateral inverse Laplace transform is $\sqrt{\pi/2}(-2c)^{-1/2}e^{-t^2/(-4c)}$. For $c> 0$ its growth on vertical lines is way too large to be a Laplace transform. – reuns Aug 26 '19 at 10:35

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