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We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillatoralgebra and study the number of its characteristics. We describe the structurefunction of deformation, analyze the classification of irreduciblerepresentations and discuss the asymptotic spectrum behaviour of theHamiltonian. For a special choice of the deformation parameters we constructthe deformed oscillator with discrete spectrum of its "quantized coordinate"operator. We establish its connection with the (generalized) discrete Hermite Ipolynomials.

Unified $(q;\alpha,\beta,\gamma;\nu)$-deformation of one-parametric q-deformed oscillator algebras