Mittag-Leffler coherent states

We create a family of boson coherent states using the functions of Mittag-Leffler (ML) E-alpha(z), (alpha > 0) and their generalizations E alpha,beta(z), (alpha, beta > 0) instead of exponentials. These states are shown to satisfy the usual requirements of normalizability, continuity in the label and the resolution of unity with a positive weight function. This last quantity is found for arbitrary alpha, beta > 0 as a solution of an associated Stieltjes moment problem. In addition, for alpha = m = 1, 2, 3 ... and beta = 1 (corresponding to E-m (z)) we propose and analyse special q-deformations (0 < q less than or equal to 1) of the functions E-m (z) which serve as a tool to define q-deformed coherent states of ML type. We provide the expressions for expectation values of physical quantities for all the above states. We discuss physical properties of these stares, noting that they are squeezed. The ML coherent states are sub-Poissonian in nature, whereas the q-deformed ML states can be sub- and super-Poissonian depending on q. All these states are shown to be eigenstares of deformed boson operators whose commutation relations are given.