The Laguerre Transform and its Applications

Abstract

Laguerre polynomials are an important family of orthogonal polynomials introduced by Edmond Laguerre in the study of differential equations. Because of their many properties, they play an important role in mathematical analysis, numerical methods, and mathematical physics. From these properties, researchers developed the Laguerre transform and its generalization through the associated Laguerre polynomials [8]. As an application of these associated polynomials, we study the associated Fibonacci and Lucas polynomials. This work is divided into three chapters. The first chapter presents some basic notions of enumerative combinatorics. The second chapter is devoted to the generalization of the Laguerre transform and the study of associated polynomials [8, 9]. Finally, the third chapter presents some applications of the Laguerre transform in different fields