Even and odd generalized hypergeometric coherent states

In this paper, we investigate a large class of generalized hypergeometric states $\mathrm{\mid }p,q,z⟩$, depending on a complex variable $z$ and two sets of parameters, $(a_1,\cdots ,a_p)$ and $(b_1,\cdots ,b_q)$. Even and odd generalized hypergeometric states $\mathrm{\mid }p,q,z{⟩}_e$ and $\mathrm{\mid }p,q,z{⟩}_o$ are also defined and analyzed. The moment problem is solved by the Mellin transform techniques. For particular values of $p$ and $q$, the photon-counting statistics, quantum optical properties and geometry of these states are discussed.