Characterizations of the Symmetric T(θ, q)-Classical Orthogonal q-Polynomials

被引：0
|
作者：
Bouras, B. [1 ]
Habbachi, Y. [1 ]
Marcellan, F. [2 ]
机构：
[1] Gabes Univ, Coll Sci, Dept Math, Gabes, Tunisia
[2] Univ Carlos III Madrid, Dept Matemat, Madrid, Spain
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2022年 / 19卷 / 02期
关键词：
Orthogonal polynomials; symmetric polynomials; q-Dunkl-classical orthogonal polynomials; regular linear functionals;
D O I：
10.1007/s00009-022-01986-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give two characterizations for symmetric q-Dunkl-classical orthogonal polynomials. The first one is related to a spectral problem for a second-order linear q-difference differential operator. The second one is given by a distribution equation of Pearson type fulfilled by their corresponding linear functionals. Then, we show that the q(2)-analogue of generalized Hermite and the q(2)-analogue of generalized Gegenbauer polynomials are, up a dilation, the only symmetric q-Dunkl-classical orthogonal polynomials.
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收藏
页数：18
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