Asymptotic expansion of thick distributions

We give a theory of asymptotic expansions of thick distributions of rapid decay at infinity. We show that the moment asymptotic expansion of standard distributions of rapid decay follows by projection of our result. We also study in which spaces of thick test functions the asymptotic Taylor approximation is valid. We employ our formulas to obtain the asymptotic expansion of several multidimensional integrals that are divergent but are regularized by using the Hadamard method.