On q-Bessel matrix polynomials

TL;DR

This paper explores properties of q-Bessel matrix polynomials, including differential equations, relations, integral transforms, and their connections to q-Horn's matrix functions, advancing the theoretical framework of q-Analysis.

Contribution

It introduces new properties and relations of q-Bessel matrix polynomials and links them to q-Horn's matrix functions, expanding the theoretical understanding in q-Analysis.

Findings

Derived q-differential matrix equations and relations

Established integral representations and transforms

Connected q-Bessel polynomials to q-Horn's matrix functions

Abstract

The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation, q-Laplace and q-Mellin transforms with the help of q-Analysis. Furthermore, we give connections between q-Horn's matrix functions of two variables and q-Bessel matrix polynomials are given.