Hypergeometric type q-difference equations:: Rodrigues type representation for the second kind solution

被引：10

作者：

Area, I

Godoy, E ^{[1
]}

Ronveaux, A

Zarzo, A

机构：

[1] Univ Vigo, Dept Matemat Aplicada 2, ETS Ingn Ind, Vigo 36200, Spain

[2] Univ Vigo, Dept Matemat Aplicada 2, ETS Telecommun, Vigo 36200, Spain

[3] Univ Catholique Louvain, Dept Math, B-1348 Louvain, Belgium

[4] Univ Granada, Fac Ciencias, Inst Carlos Fis Teor & Comp, Granada, Spain

[5] Univ Politecn Madrid, Dept Matemat Aplicada, ETS Ingn Ind, Madrid, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2005年 / 173卷 / 01期

关键词：

orthogonal polynomials; functions of the second kind; second-order q-difference equations of hypergeometric type;

D O I：

10.1016/j.cam.2004.02.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Rodrigues type representation for the second kind solution of a second-order q-difference equation of hypergeometric type is given. This representation contains some q-extensions of integrals related with relevant special functions. For these integrals, a general recurrence relation, which only involves the coefficients of the q-difference equation, is also presented. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：81 / 92

页数：12

共 50 条

[1] q-difference equations of KdV type and Chazy-type second-degree difference equations
Field, Chris M.
Joshi, Nalini
Nijhoff, Frank W.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (33)
[2] q-hypergeometric solutions of q-difference equations
Abramov, SA
Paule, P
Petkovsek, M
DISCRETE MATHEMATICS, 1998, 180 (1-3) : 3 - 22
[3] On a solution of a q-difference analogue of Lauricella's D-type hypergeometric equation with |q|=1
Nishizawa, M
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1998, 34 (03) : 277 - 290
[4] Generalizations of Rodrigues type formulas for hypergeometric difference equations on nonuniform lattices
Cheng, Jinfa
Jia, Lukun
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2020, 26 (04) : 435 - 457
[5] SOLUTION OF Q-DIFFERENCE EQUATIONS
YANG, KW
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1988, 20 : 1 - 4
[6] On q-Difference Riccati Equations and Second-Order Linear q-Difference Equations
Huang, Zhi-Bo
JOURNAL OF COMPLEX ANALYSIS, 2013,
[7] MEROMORPHIC SOLUTIONS TO COMPLEX DIFFERENCE AND q-DIFFERENCE EQUATIONS OF MALMQUIST TYPE
Zhang, Jie
Zhang, Jianjun
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
[8] Generalized q-difference equations for (q, c)-hypergeometric polynomials and some applications
Cao, Jian
Zhou, Hong-Li
Arjika, Sama
RAMANUJAN JOURNAL, 2023, 60 (04): : 1033 - 1067
[9] Weight Function Approach to q-Difference Equations for the q-Hypergeometric Polynomials
A. S. Hegazi
M. Mansour
International Journal of Theoretical Physics, 2004, 43 : 237 - 250
[10] Generalized q-difference equations for (q, c)-hypergeometric polynomials and some applications
Jian Cao
Hong-Li Zhou
Sama Arjika
The Ramanujan Journal, 2023, 60 : 1033 - 1067

← 1 2 3 4 5 →