Mathematics Faculty Articles

Title

Differential equations of some classes of special functions via the factorization method

Document Type

Article

Publication Date

12-1-2004

Publication Title

Journal of Computational Analysis and Applications

Keywords

Confluent hypergeometric functions, D-orthogonal polynomials, Differential equations, Differential operator, Factorization method, Orthogonal polynomials

ISSN

15211398

Volume

6

Issue/No.

3

First Page

265

Last Page

275

Abstract

Let {P n(x)} n=0∞ be a sequence of polynomials of degree n. We define two sequences of differential operators Φ n and ψ n satisfying the following properties Φ n(P n(x))=P n-1(x), Ψ n(Pn(x)) = P n+1(x). By constructing these two operators for some classes of special functions, we determine their differential equations via the factorization method introduced in [3]. We illustrate our method by including classical orthogonal polynomials, d-orthogonal polynomials, confluent hypergeometric functions and hypergeometric functions as the applications. Copyright 2004 Eudoxus Press, LLC.

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