  We introduce a large class of holomorphic quantum states by choosing their
normalization functions to be given by generalized hypergeometric functions. We
call them generalized hypergeometric states in general, and generalized
hypergeometric coherent states in particular, if they allow a resolution of
unity. Depending on the domain of convergence of the generalized hypergeometric
functions, we distinguish generalized hypergeometric states on the plane, the
open unit disk, and the unit circle. All states are eigenstates of suitably
defined lowering operators. We then study their photon number statistics and
phase properties as revealed by the Husimi and Pegg-Barnett phase
distributions. On the basis of the generalized hypergeometric coherent states
we introduce generalized hypergeometric Husimi distributions and corresponding
phase distributions as well as new analytic representations of arbitrary
quantum states in Bargmann and Hardy spaces.
