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

Authors

Matthew X. He, Nova Southeastern UniversityFollow
Paolo E. Ricci, Sapienza Università di Roma

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.

NSUWorks Citation

He, Matthew X. and Ricci, Paolo E., "Differential equations of some classes of special functions via the factorization method" (2004). Mathematics Faculty Articles. 331.
https://nsuworks.nova.edu/math_facarticles/331