On the q-Charlier Multiple Orthogonal Polynomials

被引：7

作者：

Arvesu, Jorge ^{[1
]}

Ramirez-Aberastruris, Andys M. ^{[1
]}

机构：

[1] Univ Carlos III Madrid, Dept Math, Leganes 28911, Spain

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2015年 / 11卷

关键词：

multiple orthogonal polynomials; Hermite-Pade approximation; difference equations; classical orthogonal polynomials of a discrete variable; Charlier polynomials; q-polynomials; ASYMPTOTICS; ZEROS;

D O I：

10.3842/SIGMA.2015.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：14

共 20 条

[11] Interlacing properties of zeros of multiple orthogonal polynomials
Haneczok, Maciej
Van Assche, Walter
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (01) : 429 - 438
[12] Koekoek R., 2010, SPRINGER MONOGR MATH
[13] Difference equations for discrete classical multiple orthogonal polynomials
Lee, D. W.
[J]. JOURNAL OF APPROXIMATION THEORY, 2008, 150 (02) : 132 - 152
[14] Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
Miki, Hiroshi
Vinet, Luc
Zhedanov, Alexei
[J]. PHYSICS LETTERS A, 2011, 376 (02) : 65 - 69
[15] Asymptotics for the ratio and the zeros of multiple Charlier polynomials
Ndayiragije, Francois
Van Assche, Walter
[J]. JOURNAL OF APPROXIMATION THEORY, 2012, 164 (06) : 823 - 840
[16] Nikishin E.M., 1991, Translations of Mathematical Monographs, V92
[17] Multiple little q-Jacobi polynomials
Postelmans, K
Van Assche, W
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 178 (1-2) : 361 - 375
[18] Remainder Pade approximants for the exponential function
Prevost, Marc
Rivoal, Tanguy
[J]. CONSTRUCTIVE APPROXIMATION, 2007, 25 (01) : 109 - 123
[19] Difference equations for multiple Charlier and Meixner polynomials
Van Assche, W
[J]. PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON DIFFERENCE EQUATIONS: NEW PROGRESS IN DIFFERENCE EQUATIONS, 2004, : 549 - 557
[20] Nearest neighbor recurrence relations for multiple orthogonal polynomials
Van Assche, Walter
[J]. JOURNAL OF APPROXIMATION THEORY, 2011, 163 (10) : 1427 - 1448

← 1 2 →