On the recurrence coefficients of generalized little $q$-Laguerre polynomials

TL;DR

This paper investigates a semi-classical variation of the weight for little q-Laguerre polynomials, deriving a discrete equation governing their recurrence coefficients.

Contribution

It introduces a new semi-classical weight variation and derives a second order second degree discrete equation for the recurrence coefficients.

Findings

Derived a discrete equation for recurrence coefficients.

Extended understanding of semi-classical q-Laguerre polynomials.

Provides a basis for further analytical and numerical studies.

Abstract

In this paper we consider a semi-classical variation of the weight related to the little $q$-Laguerre polynomials and obtain a second order second degree discrete equation for the recurrence coefficients in the three-term recurrence relation.