Is there a general expression for laplace transform of exponential of a function? i.e.
$\mathcal{L}\left(e^{x\left(t\right)}\right)$
where x is a function of t and the transformation is from the time domain variable t to the frequeny domain variable s. I can approximate it with taylor's series for a given x, but I would like to know if a general, exact formula for it exists. More specifically, I would like to express the time-domain system
$y(t)=e^{x(t)}$
as
$Y\left(s\right)=T\left(s\right)X\left(s\right)$
where
$X\left(s\right)=$ Laplace transform of x(t),
$Y\left(s\right)=$ Laplace transform of y(t) and
$T\left(s\right)=$ Transfer function of the system.
Best Answer
There are some special cases of the Laplace transforms of composite functions. See this document and this one.