A convergence theorem for asymptotic expansions of Feynman amplitudes

The Mellin representation of Feynman integrals is revisited. From this representation, an asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to infinity, may be obtained. In the case of all masses going to zero in a Euclidean metric, we show that the truncated expansion has a remainder which is compatible with convergence of the series.