On the completeness of photon-added coherent states

We demonstrate explicitly the completeness of photon-added coherent states (PACSs), introduced by Agarwal and Tara (Agarwal G S and Tara K 1991 Phys. Rev. A 43 492) and defined, up to normalization, by ((a) over cap (dagger))(M) \z], M = 0, 1, 2,..., where (a) over cap (dagger) is the boson creation operator and \z] are conventional Glauber-Klauder coherent states. We find the analytical form of the positive weight function in their resolution of unity by solving the associated Stieltjes power-moment problem. We furnish an example of generation of another set of PACSs which are complete.