Mittag-Leffler coherent states

We create a family of boson coherent states using the functions of Mittag-L effler (ML) E-alpha(z), (alpha > 0) and their generalizations E alpha,beta( z), (alpha, beta > 0) instead of exponentials. These states are shown to sa tisfy the usual requirements of normalizability, continuity in the label an d the resolution of unity with a positive weight function. This last quanti ty is found for arbitrary alpha, beta > 0 as a solution of an associated St ieltjes 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 expres sions for expectation values of physical quantities for all the above state s. We discuss physical properties of these stares, noting that they are squ eezed. The ML coherent states are sub-Poissonian in nature, whereas the q-d eformed ML states can be sub- and super-Poissonian depending on q. All thes e states are shown to be eigenstares of deformed boson operators whose comm utation relations are given.