The Laplace transform $\int_0^\infty e^{-tx} f(t) dt$ is for large $x$ asymptotically equivalent to $\sum_{n=0}^\infty \frac{f^{(n)}(0)}{x^{n+1}}$ (Watson's lemma).
Given that the Laplace transform converges everywhere, is there a similar formula for $x \to -\infty$?