On the q-Charlier Multiple Orthogonal Polynomials

We introduce a new family of special functions, namely q-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to q-analogues of Poisson distributions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained. An explicit representation in terms of a q-analogue of the second of Appell's hypergeometric functions is given. A high-order linear q-difference equation with polynomial coefficients is deduced. Moreover, we show how to obtain the nearest neighbor recurrence relation from some difference operators involved in the Rodrigues-type formula.

multiple orthogonal polynomials; hermite-padé approximation; difference equations; classical orthogonal polynomials of a discrete variable; charlier polynomials; q-polynomials

On the q-Charlier Multiple Orthogonal Polynomials Articles