We establish some new properties and identities of Generalized Gaussian
Numbers (GGN) which is defined recently in [10, 11] parallel to those of
Gaussian coefficients. We present generating functions and some properties
which are very useful for GGN. We obtain some family of sequences
which are unimodal and present the log-concavity property of GGN. Finally,
we give a connection of GGN to the Rogers-Szegö polynomials.