Meixner Polynomials and ID Para-Bose Oscillator

In this paper, the matrix elements of the para-squeeze operator in the eigenstate basis of the para-Bose oscillator are computed explicitly. These matrix elements are seen to involve the Meixner polynomials. The underlying framework allows for the systematic derivation of the recurrence relations, difference equation, lowering and rising operators and generating functions which these polynomials satisfy.