  In this paper, we investigate a large class of generalized hypergeometric
states $|p,q,z\rangle$, 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 $|p,q,z\rangle_e$ and $|p,q,z\rangle_o$ 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.
