Abstract
The main purpose of this paper is to investigate a generalized oscillator algebra, naturally associated to the Levy-Meixner polynomials and a class of nonlinear coherent vector. We derive their overcompleteness relation, in so doing, the partition of the unity in terms of the eigenstates of the sequences of coherent vectors is established. An example of complex hypercontractivity property for an Hamiltonian is developed to illustrate our theory.