Differential Equation of Appell Polynomials Via the Factorization Method

Authors

Matthew He, Nova Southeastern UniversityFollow
Paolo E. Ricci, Università degli Studi di Roma “La Sapienza”

Document Type

Article

Publication Date

2-15-2002

Publication Title

Journal of Computational and Applied Mathematics

Keywords

Appell polynomials, Bernoulli polynomials, Euler polynomials, Differential equations

ISSN

0377-0427

Volume

139

Issue/No.

2

First Page

231

Last Page

237

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:

By constructing these two operators for Appell polynomials, we determine their differential equations via the factorization method introduced by Infeld and Hull (Rev. Mod. Phys. 23 (1951) 21). The differential equations for both Bernoulli and Euler polynomials are given as special cases of the Appell polynomials.

Comments

MSC

• 33C45;
• 33C55

Under an Elsevier user license

NSUWorks Citation

He, Matthew and Ricci, Paolo E., "Differential Equation of Appell Polynomials Via the Factorization Method" (2002). Mathematics Faculty Articles. 172.
https://nsuworks.nova.edu/math_facarticles/172

DOI

10.1016/S0377-0427(01)00423-X