The generating function of bivariate Chebyshev polynomials associated with the Lie algebra $G_2$

TL;DR

This paper constructs the generating function for bivariate Chebyshev polynomials linked to the Lie algebra G2, expanding the mathematical tools available for studying these special functions.

Contribution

It introduces a new generating function for G2-associated Chebyshev polynomials using a method from prior research, advancing the theoretical understanding.

Findings

Explicit form of the generating function derived

Method applicable to other Lie algebra-related polynomials

Enhances analytical tools for Chebyshev polynomials

Abstract

The generating function of the second kind bivariate Chebyshev polynomials associated with the simple Lie algebra $G_2$ is constructed by the method proposed in \cite{DKS} and \cite{DKS1}.