Differential Equation of Appell Polynomials Via the Factorization Method

Matthew He; Paolo E. Ricci

doi:10.1016/S0377-0427(01)00423-X

Differential Equation of Appell Polynomials Via the Factorization Method

Matthew He
, Paolo E. Ricci

Research output: Contribution to journal › Article › peer-review

85 Scopus citations

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.

Original language	American English
Pages (from-to)	231-237
Number of pages	7
Journal	Journal of Computational and Applied Mathematics
Volume	139
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(01)00423-X
State	Published - Feb 15 2002

Funding

This paper was concluded on a visit of the first author to the Dipartimento di Matematica, Università degli Studi di Roma “La Sapienza”, Italy, whose hospitality and partial support from the Italian National Research Council (G.N.I.M.) we wish to acknowledge.

Funders
Dipartimento di Matematica
Universita degli Studi di Roma "La Sapienza"
Consiglio Nazionale delle Ricerche

ASJC Scopus Subject Areas

Computational Mathematics
Applied Mathematics

Keywords

Appell polynomials
Bernoulli polynomials
Differential equations
Euler polynomials

Disciplines

Mathematics

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Differential Equation of Appell Polynomials Via the FactorizationFinal published version, 146 KBLicense: Unspecified

Cite this

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title = "Differential Equation of Appell Polynomials Via the Factorization Method",

abstract = "Let \{Pn(x)\}∞n=0 be a sequence of polynomials of degree n. We define two sequences of differential operators Φn and Ψn 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.",

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T1 - Differential Equation of Appell Polynomials Via the Factorization Method

AU - He, Matthew

AU - Ricci, Paolo E.

PY - 2002/2/15

Y1 - 2002/2/15

N2 - Let {Pn(x)}∞n=0 be a sequence of polynomials of degree n. We define two sequences of differential operators Φn and Ψn 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.

AB - Let {Pn(x)}∞n=0 be a sequence of polynomials of degree n. We define two sequences of differential operators Φn and Ψn 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.

KW - Appell polynomials

KW - Bernoulli polynomials

KW - Differential equations

KW - Euler polynomials

UR - https://nsuworks.nova.edu/math_facarticles/172

UR - https://www.scopus.com/pages/publications/0037083038

UR - https://www.scopus.com/pages/publications/0037083038#tab=citedBy

U2 - 10.1016/S0377-0427(01)00423-X

DO - 10.1016/S0377-0427(01)00423-X

M3 - Article

SN - 0377-0427

VL - 139

SP - 231

EP - 237

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Differential Equation of Appell Polynomials Via the Factorization Method

Abstract

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ASJC Scopus Subject Areas

Keywords

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