Smoothness and analyticity of perturbation expansions in qed

We consider the ground state of an atom in the framework of non-relativistic qed. We assume that the ultraviolet cutoff is of the order of the Rydberg energy and that the atomic Hamiltonian has a non-degenerate ground state. We show that the ground state energy and the ground state are k-times continuously differentiable functions of the fine structure constant and respectively the square root of the fine structure constant on some nonempty interval [0,ck).