On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials

被引：5

作者：

Koornwinder, Tom H. ^{[1
]}

机构：

[1] Univ Amsterdam, Korteweg de Vries Inst, NL-1090 GE Amsterdam, Netherlands

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2011年 / 7卷

关键词：

Askey scheme; q-Askey scheme; q-Racah polynomials; big q-Jacobi polynomials; multi-parameter limit;

D O I：

10.3842/SIGMA.2011.040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey-Wilson to Wilson polynomials and from q-Racah to Racah polynomials are given in a more conceptual way.

引用

页数：8

共 50 条

[41] The connection problem associated with a Selberg type integral and the q-Racah polynomials
Mimachi, Katsuhisa
[J]. FORUM MATHEMATICUM, 2013, 25 (06) : 1127 - 1179
[42] ORTHOGONAL POLYNOMIALS IN 2 VARIABLES OF Q-HAHN AND Q-JACOBI TYPE
DUNKL, CF
[J]. SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1980, 1 (02): : 137 - 151
[43] Recurrence relations of the multi-indexed orthogonal polynomials V: Racah and q-Racah types
Odake, Satoru
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2019, 60 (02)
[44] On q-orthogonal polynomials over a collection of complex origin intervals related to little q-Jacobi polynomials
Rajkovic, Predrag M.
Marinkovic, Sladjana D.
Stankovic, Miomir S.
[J]. RAMANUJAN JOURNAL, 2006, 12 (02): : 245 - 255
[45] On q-orthogonal polynomials over a collection of complex origin intervals related to little q-Jacobi polynomials
Predrag M. Rajković
Sladjana D. Marinković
Miomir S. Stanković
[J]. The Ramanujan Journal, 2006, 12 : 245 - 255
[46] CONTIGUOUS RELATIONS, BASIC HYPERGEOMETRIC-FUNCTIONS, AND ORTHOGONAL POLYNOMIALS .2. ASSOCIATED BIG Q-JACOBI POLYNOMIALS
GUPTA, DP
ISMAIL, MEH
MASSON, DR
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 171 (02) : 477 - 497
[47] A classical model for perfect transfer and fractional revival based on q-Racah polynomials
Scherer, Hugo
Vinet, Luc
Zhedanov, Alexei
[J]. PHYSICS LETTERS A, 2022, 431
[48] NONNEGATIVE KERNELS IN PRODUCT-FORMULAS FOR Q-RACAH POLYNOMIALS .1.
GASPER, G
RAHMAN, M
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1983, 95 (02) : 304 - 318
[49] Coupling coefficients of suq(1,1) and multivariate q-Racah polynomials
Genest, Vincent X.
Iliev, Plamen
Vinet, Luc
[J]. NUCLEAR PHYSICS B, 2018, 927 : 97 - 123
[50] Irrationality proof of a q-extension of ζ(2) using little q-Jacobi polynomials
Smet, Christophe
Van Assche, Walter
[J]. ACTA ARITHMETICA, 2009, 138 (02) : 165 - 178

← 1 2 3 4 5 →