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.

引用

页数：18

共 21 条

[1]

Abdelkarim F., 1997, Results Math, V32, P1

[2] Characterization of q-Dunkl-classical symmetric orthogonal q-polynomials [J].