Fourth-order difference equation for the associated Meixner and Charlier polynomials (Q1919960)

An explicit representation of the associated Meixner polynomials (with a real association parameter \(\gamma\geq 0\)) is given in terms of hypergeometric functions. This representation allows to derive the fourth-order difference equation satisfied by these polynomials. 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.