Inverse Laplace Transform of Bessel Function What is the inverse Laplace transform of $I_{0}(2 s)$ where $I_{0}(x)$ is the zeroth order Bessel function?

The modified Bessel function $I_0(2s)$ is an increasing function of $s$.  The asymptotic expansion is given by 
$$
I_0(z) \sim \frac{e^z}{\sqrt{2\pi z}} \quad \text{as } z\rightarrow\infty \; .$$
So, the inverse transform does not exist in the "usual sense''.
