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Mathematics Faculty Articles
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.
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
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