  We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillator
algebra and study the number of its characteristics. We describe the structure
function of deformation, analyze the classification of irreducible
representations and discuss the asymptotic spectrum behaviour of the
Hamiltonian. For a special choice of the deformation parameters we construct
the deformed oscillator with discrete spectrum of its "quantized coordinate"
operator. We establish its connection with the (generalized) discrete Hermite I
polynomials.
