Special Function Representation Of Dickson Polynomials

TL;DR

This paper derives generating functions and functional equations for Dickson polynomials, expressing them through incomplete gamma functions and evaluating special cases with mathematical constants, advancing their analytical understanding.

Contribution

It introduces new representations of Dickson polynomials using incomplete gamma functions and explores their analytical properties.

Findings

Derived generating functions and functional equations for Dickson polynomials.

Expressed these functions in terms of incomplete gamma functions.

Evaluated special cases involving composite incomplete gamma functions and constants.

Abstract

Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the parameters involved. Special cases are evaluated in terms of composite incomplete gamma functions and mathematical constants.