# Are there inverse Mellin transforms with two distinct strips of convergence?

Let

$$F(x)=\frac{1}{2\pi i}\int\limits_{c-i\infty}^{c+i\infty}f(s)x^{-s}ds$$

$$f(s)=\int\limits_{0}^{\infty}F(x)x^{s-1}dx$$

Real constant $c$ is from the strip $\Re(s)\in(a,b)$.

$\textbf{Question}$: Is there a function $f(s)$ such that $\int_{c-i\infty}^{c+i\infty}f(s)x^{-s}ds$ converges on two strips $S_1$ and $S_2$ such that $S_1\cap S_2=\emptyset$, for any real $c$ from $S_1 \cup S_2$?