On the $q$-Charlier Multiple Orthogonal Polynomials

[摘要] 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.

[关键词] multiple orthogonal polynomials;Hermite–Pad´e approximation;dif ference equations;classical orthogonal polynomials of a discrete variable;Charlier polynomials;q-polynomials