Discrete Orthogonal Polynomials with Hypergeometric Weights and Painleve VI

被引：14

作者：

Filipuk, Galina ^{[1
]}

Van Assche, Walter ^{[2
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Banacha 2, PL-02097 Warsaw, Poland

[2] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B,Box 2400, BE-3001 Leuven, Belgium

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

discrete orthogonal polynomials; hypergeometric weights; discrete Painleve equations; Painleve VI; RECURRENCE COEFFICIENTS; EQUATIONS;

D O I：

10.3842/SIGMA.2018.088

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second order differential equation in one of the parameters of the weights. The non-linear difference equations form a pair of discrete Painleve equations and the differential equation is the sigma-form of the sixth Painleve equation. We briefly investigate the asymptotic behavior of the recurrence coefficients as n -> infinity using the discrete Painleve equations.

引用

页数：19

共 50 条

[21] THE ELECTROSTATIC EQUILIBRIUM PROBLEM FOR CLASSICAL DISCRETE ORTHOGONAL POLYNOMIALS [J].

Rutka, Przemyslaw ;

Smarzewski, Ryszard .

MATHEMATICS OF COMPUTATION, 2023, 92 (341) :1331-1348

[22] Nonlinear equations for the recurrence coefficients of discrete orthogonal polynomials [J].

Ismail, Mourad E. H. ;

Simeonov, Plamen .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 376 (01) :259-274

[23] A characterization of the classical orthogonal discrete and q-polynomials [J].

Alfaro, M. ;

Alvarez-Nodarse, R. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 201 (01) :48-54

[24] Discrete orthogonal polynomials and difference equations of several variables [J].

Iliev, Plamen ;

Xu, Yuan .

ADVANCES IN MATHEMATICS, 2007, 212 (01) :1-36

[25] The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights [J].

Kuijlaars, A. B. J. ;

Tibboel, P. M. J. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 233 (03) :775-785

[26] Pearson equations for discrete orthogonal polynomials: III-Christoffel and Geronimus transformations [J].

Manas, Manuel .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2022, 116 (04)

[27] Discrete semi-classical orthogonal polynomials of class one on quadratic lattices [J].

Filipuk, G. ;

Rebocho, M. N. .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2019, 25 (01) :1-20

[28] Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems [J].

Miki, Hiroshi ;

Goda, Hiroaki ;

Tsujimoto, Satoshi .

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2012, 8

[29] Multiparameter discrete transforms based on discrete orthogonal polynomials and their application to image watermarking [J].

Annaby, M. H. ;

Ayad, H. A. ;

Prestin, Juergen ;

Rushdi, Muhammad A. .

SIGNAL PROCESSING-IMAGE COMMUNICATION, 2021, 99

[30] The generalized Krawtchouk polynomials and the fifth Painleve equation [J].

Boelen, Lies ;

Filipuk, Galina ;

Smet, Christophe ;

Van Assche, Walter ;

Zhang, Lun .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2013, 19 (09) :1437-1451

← 1 2 3 4 5 →