What is the inverse Laplace transform of $I_{0}(2 s)$ where $I_{0}(x)$ is the zeroth order Bessel function?
2026-04-02 10:08:23.1775124503
Inverse Laplace Transform of Bessel Function
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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''.