The quasi-antisymmetric $D_{-w}$-Laguerre-Hahn orthogonal polynomials of class one

Abstract

In this work, we solve the system of Laguerre-Freud equations for the recurrence coefficients $\zeta_n$, $\theta_{n+1} , n \geq 0,$ of the $D_{w}$-Laguerre-Hahn orthogonal sequences of polynomials of class one in the case when $\zeta_{0}=-\alpha_{0}$, $\zeta_{n+1}=\alpha_{n}-\alpha_{n+1}$ and $\theta_{n+1}=-\alpha_{n}^{2}$ with $\alpha_{n}\neq0\;n\geq0$, where $D_w$ is the divided difference operator. There are essentially six canonical cases.

В роботі розв'язано систему рівнянь Лагерра-Фрейда для рекурентних коефіцієнтів $ \zeta_n$, $ \theta_{n+1}, n \geq0, $ послідовностей ортогональних $ D_{w} $-многочленів Лагерра-Хана першого роду у випадку, коли $ \zeta_{0}= - \alpha_{0}$, $ \zeta_{n+1}= \alpha_{n}- \alpha_{n+1} $ і $ \theta_{n+1}=- \alpha_{n}^{2} $ з $ \alpha_{n} \neq0$, $n \geq0$, де $ D_w $ є оператором розділеної різниці. Встановлено шість канонічних випадків.

Key words: Discrete Laguerre-Hahn orthogonal polynomials, Difference operator.

Full Text

Article Information

Title	The quasi-antisymmetric $D_{-w}$-Laguerre-Hahn orthogonal polynomials of class one
Source	Methods Funct. Anal. Topology, Vol. 30 (2024), no. 1-2, 80-100
DOI	10.31392/MFAT-npu26_1-2.2024.08
Copyright	The Author(s) 2024 (CC BY-SA)

Authors Information

Mohamed Zatra
University of Gabes, Higher Institute of Water Sciences and Techniques of Gabes, Research Laboratory of Mathematics and Applications, LR17ES11, 6072, Gabes, Tunisia.

Safa Dekhil
University of Gabes, Faculty of Sciences of Gabes, Research Laboratory of Mathematics and Applications, LR17ES11, 6072, Gabes, Tunisia.

Citation Example

Mohamed Zatra and Safa Dekhil, The quasi-antisymmetric $D_{-w}$-Laguerre-Hahn orthogonal polynomials of class one, Methods Funct. Anal. Topology 30 (2024), no. 1, 80-100.

BibTex

@article {MFAT2009,
    AUTHOR = {Mohamed Zatra and Safa Dekhil},
     TITLE = {The quasi-antisymmetric $D_{-w}$-Laguerre-Hahn orthogonal
  polynomials of class
  one},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {30},
      YEAR = {2024},
    NUMBER = {1},
     PAGES = {80-100},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_1-2.2024.08},
       URL = {http://mfat.imath.kiev.ua/article/?id=2009},
}

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