Symmetry Integrability and Geometry-Methods and Applications | |
On the $q$-Charlier Multiple Orthogonal Polynomials | |
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
【 预 览 】
Files | Size | Format | View |
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RO202106300001256ZK.pdf | 388KB | download |