2014/11/30 by J. Arvesú, Jorge Arvesú, Andys M. Ramírez-Aberasturis · 6 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Classical orthogonal polynomials #Difference polynomials #Discrete orthogonal polynomials #Gegenbauer polynomials #Hahn polynomials #Hypergeometric distribution #Hypergeometric function #Jacobi polynomials #Kravchuk polynomials #Mathematical functions and polynomials #Mathematics #Orthogonal polynomials #Poisson distribution #Pure mathematics #Type (biology) #Wilson polynomials #math.CA
paper · pdf · doi:10.3842/sigma.2015.026
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
arxiv created 2015/03/28 · openalex publication_date 2015/03/28 · arxiv updated 2015/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.