# Bivariate degenerate Hermite polynomials in the framework of Lie algebra K5

## TL;DR

This paper explores the matrix representations of the 5-dimensional Lie algebra K5 and introduces new results on bivariate degenerate Hermite polynomials within this algebraic framework, including formulas and integral equations.

## Contribution

It provides the first matrix element representations of the K5 Lie algebra and connects these to bivariate degenerate Hermite polynomials using Lie algebraic methods.

## Key findings

- Matrix elements of K5 Lie algebra obtained for the first time
- Explicit formulas for bivariate degenerate Hermite polynomials derived
- Integral equations for these polynomials explored

## Abstract

In this article, the matrix elements of a representation of the 5-dimensional Lie algebra K5 are obtained for the first time. The bivariate degenerate Hermite polynomials Hm(z1, z2|{\tau} ) are considered within the context of this representation. Further, employing the Lie algebraic techniques, certain specific results concerning these polynomials are established.Some examples providing the implicit formulas for the polynomials related to the polynomials Hm(z1, z2|{\tau} ) are considered. Integral equations for these polynomials are also explored.