The q-Meixner distributions associated with a q-deformed symmetric Fock space

Abstract

In this paper, we consider the self-adjoint operator of the linear sum of the double q-creation, the double q-annihilation, the q-number, and the scalar operators on a q-deformed symmetric Fock space and investigate its distribution. By the self-adjointness of the operator, the theory of orthogonal polynomials can help us to determine the distributions well. It will be found that the distributions are in the types of the q-Meixner family.