The Mellin transform of a function $f(x)$ can be written as

$$ \mathcal M[f(x);z]=\int_0^\infty f(x)x^{z-1} dx $$

Is there a simple expression for the Mellin transform of the function $f(x-x_0)$? For example

$$ \mathcal M[e^{-x^2}] = \frac{1}{2}\Gamma\left(\frac{z}{2}\right) $$

What would $\mathcal M[e^{-(x-x_0)^2}]$ or more generally $\mathcal M[e^{-(x-x_0)^n}]$ be? This may, for example, find application in the Mellin transform of the Gaussian probability density function.