Matrix-valued little q-Jacobi polynomials

被引：4

作者：

Aldenhoven, Noud ^{[1
]}

Koelink, Erik ^{[1
]}

de los Rios, Ana M. ^{[2
]}

机构：

[1] Radboud Univ Nijmegen, IMAPP, FNWI, NL-6525 AJ Nijmegen, Netherlands

[2] Univ Seville, Dept Anal Matemat, E-41080 Seville, Spain

来源：

JOURNAL OF APPROXIMATION THEORY | 2015年 / 193卷

关键词：

Matrix-valued orthogonal polynomials; Little q-Jacobi polynomials; Matrix-valued q-difference operators; THEOREM;

D O I：

10.1016/j.jat.2014.10.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2 x 2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and their relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on a matrix-valued q-difference operator, which is a q-analogue of Tirao's matrix-valued hypergeometric differential operator. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：164 / 183

页数：20

共 50 条

[1] Multivariable big and little q-Jacobi polynomials
Stokman, JV
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (02) : 452 - 480
[2] A class of matrix-valued polynomials generalizing Jacobi polynomials
Costin, Rodica D.
JOURNAL OF APPROXIMATION THEORY, 2009, 161 (02) : 787 - 801
[3] On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials
Atakishiyev, NM
Klimyk, AU
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 294 (01) : 246 - 257
[4] A Simple Proof of a Congruence for a Series Involving the Little q-Jacobi Polynomials
Dixit, Atul
ANNALS OF COMBINATORICS, 2019, 23 (3-4) : 713 - 716
[5] Interlacing properties and bounds for zeros of hypergeometric and little q-Jacobi polynomials
Gochhayat, P.
Jordaan, K.
Raghavendar, K.
Swaminathan, A.
RAMANUJAN JOURNAL, 2016, 40 (01) : 45 - 62
[6] Irrationality proof of a q-extension of ζ(2) using little q-Jacobi polynomials
Smet, Christophe
Van Assche, Walter
ACTA ARITHMETICA, 2009, 138 (02) : 165 - 178
[7] Non-classical orthogonality relations for big and little q-Jacobi polynomials
Moreno, Samuel G.
Garcia-Caballero, Esther M.
JOURNAL OF APPROXIMATION THEORY, 2010, 162 (02) : 303 - 322
[8] Irrationality proof of certain Lambert series using little q-Jacobi polynomials
Coussement, J.
Smet, C.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 233 (03) : 680 - 690
[9] Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials
Kar, Pinaki Prasad
Gochhayat, Priyabrat
NUMERICAL ALGORITHMS, 2023, 93 (03) : 1157 - 1170
[10] Generalized little q-Jacobi polynomials as eigensolutions of higher-order q-difference operators
Vinet, L
Zhedanov, A
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (05) : 1317 - 1327

← 1 2 3 4 5 →