Fourth-order difference equation for co-recursive associated Meixner and Charlier polynomials (Q5946618)

The author presents an explicit representation in terms of hypergeometric functions of the co-recursive associated Meixner polynomials that arise from the Chapman-Kolmogorov equation of linear birth and death processes. He derives a fourth-order difference equation, a generating function, and the Stieltjes transform of the orthogonality measure. He also investigates certain limiting cases that arise in solving the equations of particular linear birth and death processes.