On the $q$-Charlier Multiple Orthogonal Polynomials

Symmetry Integrability and Geometry-Methods and Applications

article

Jorge Arvesú¹  Andys M. Ramírez-Aberasturis¹ 

[1] Department of Mathematics, Universidad Carlos III de Madrid, Avenida de la Universidad

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

DOI  :  10.3842/SIGMA.2015.026

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown