An Introduction to the q-Laguerre-Hahn Orthogonal q-Polynomials
Abdallah Ghressi, Lotfi Kh\'eriji, Mohamed Ihsen Tounsi
TL;DR
This paper introduces a generalization of q-Laguerre-Hahn orthogonal q-polynomials, exploring their properties via q-difference equations, class criteria, and structure relations, with illustrative examples.
Contribution
It provides a new framework for understanding q-Laguerre-Hahn polynomials through q-difference equations and class criteria, expanding the theory of orthogonal q-polynomials.
Findings
Derived the q-Riccati equation for the formal Stieltjes series
Established the structure relation for the polynomials
Provided illustrative examples demonstrating the theory
Abstract
Orthogonal q-polynomials associated with q-Laguerre-Hahn form will be studied as a generalization of the q-semiclassical forms via a suitable q-difference equation. The concept of class and a criterion to determinate it will be given. The q-Riccati equation satisfied by the corresponding formal Stieltjes series is obtained. Also, the structure relation is established. Some illustrative examples are highlighted.
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