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.