# Can asymptotic of a Mellin (or laplace inverse ) be evaluated?

I mean, given the Mellin inverse integral $\int_{c-i\infty}^{c+i\infty}dsF(s)x^{-s}$, can we evaluate this integral, at least as $x \rightarrow \infty$?

Can the same be made for $\int_{c-i\infty}^{c+i\infty}dsF(s)\exp(st)$ as $x \rightarrow \infty$?

Why or why not can this be evaluated in order to get the asymptotic behaviour of Mellin inverse transforms?

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$F(s)= \frac{1}{\zeta(s)}$ , the problem here is the infinite number of poles of $F(s)$ – Jose Garcia Apr 20 '12 at 9:28