Fourth-order difference equation for the associated Meixner and Charlier polynomials

摘要

An explicit representation of the associated Meixner polynomials (with a real association parameter 0) is given in terms of hypergeometric functions. This representation allows to derive the fourth-order difference equation verified by these polynomials. Appropriate limits give the fourth-order difference equation for the associated Charlier polynomials and the fourth-order differential equations for the associated Laguerre and Hermite polynomials.