一级对称 $$H_q$$ -Laguerre-Hahn 正交 q 多项式的描述

IF 0.6 3区 数学 Q3 MATHEMATICS
Sobhi Jbeli
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引用次数: 0

摘要

我们研究的是\(H_{q}\)-拉盖尔-哈恩形式u,即那些满足多项式系数(\(\Phi , \Psi , B\) )的q-二次q-差分方程的形式:\( H_{q}(\Phi (x)u) +\Psi (x) u+B(x) \, \big (x^{-1}u(h_{q}u)\big )=0,\) 其中 \(h_q u\) 是由((langle h_{q} u、f(qx)\rangle \)对于所有多项式 f 而言都是定义的形式,而 \(H_{q}\)是 q 衍生算子。我们给出了这种形式的类 s 的定义,并通过结构关系描述了其对应的正交 q 多项式序列 \(\{P_n\}_{n\ge 0}\)。因此,我们为对称情况下的类一建立了由结构关系系数、多项式系数(\Phi , \Psi , B\ )和 \(\gamma _{n+1}, \, n \ge 0\) 的递推系数(\(\{P_n\}_{n\ge 0}\ )满足的系统。此外,我们还完整地描述了类\(s=1.\)的对称\(H_{q}\)-拉盖尔-哈恩形式的极限情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Description of the symmetric $$H_q$$ -Laguerre–Hahn orthogonal q-polynomials of class one

We study the \(H_{q}\)-Laguerre–Hahn forms u, that is to say those satisfying a q-quadratic q-difference equation with polynomial coefficients (\(\Phi , \Psi , B\)): \( H_{q}(\Phi (x)u) +\Psi (x) u+B(x) \, \big (x^{-1}u(h_{q}u)\big )=0,\) where \(h_q u\) is the form defined by \(\langle h_{q} u,f\rangle =\langle u, f(qx)\rangle \) for all polynomials f and \(H_{q}\) is the q-derivative operator. We give the definition of the class s of such a form and the characterization of its corresponding orthogonal q-polynomials sequence \(\{P_n\}_{n\ge 0}\) by the structure relation. As a consequence, we establish the system fulfilled by the coefficients of the structure relation, those of the polynomials \(\Phi , \Psi , B\) and the recurrence coefficient \(\gamma _{n+1}, \, n \ge 0\), of \(\{P_n\}_{n\ge 0}\) for the class one in the symmetric case. In addition, we present the complete description of the symmetric \(H_{q}\)-Laguerre–Hahn forms of class \(s=1.\) The limiting cases are also covered.

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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.
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