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?