On the ω-Multiple Charlier Polynomials

Abstract

ABSTRACT: Appell polynomials are certain family having wide range of application areas from numerical analysis to analytic function theory. They were defined by Paul Emile Appell in 1880. The most famous Appell polynomials are Hermite, Bernoulli and Euler polynomials. This thesis consists of five chapters. Chapter 1 is devoted to ntroduction. In Chapter 2, we give basic definitions and properties that is used throughout the thesis. Chapters 3, 4 and 5 are original. In Chapter 3, we introduce 3D-ω-Hermite Appell polynomials An (x, y,z;ω) using ω-Hermite polynomials Gω n (x, y,z). We obtain their explicit forms, determinantal representations, recurrence relations, lowering and raising operators, difference equations, integro-difference equations, and partial difference equations. In Chapter 4, we introduce the ∆ω-multiple Appell polynomials and we give an explicit representation and recurrence relations for them. In the last chapter, we define ω-multiple Charlier polynomials then we give raising operator, Rodrigues formula, explicit representation and generating function. Also an (r +1)th order difference equation is given. As an example we consider the case ω = 3 2 and define 3 2−multiple Charlier polynomials. Keywords: ∆ω-Appell polynomials, determinant, recurrence equation, Multiple orthogonal polynomials, ω- multiple Charlier polynomials, Appell polynomials, Hypergeometric function, Rodrigues formula, Generating function, Difference equation