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

Question

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.

Answer 1

yes we can evaluate above integral but it depends on F(s).what is your F(s).then we can see how to solve it.above integral is inverse mellin transform.Some times it is v difficult to find inverse,it all depends on what F(s) is.