Differential equation of Appell polynomials via the factorization method

Authors:
M. X. He;P. E. Ricci
Affiliations:
Department of Mathematics, Nova Southeastern University, 3301 College Avenue, Fort Lauderdale, FL;Dipartimento di Matematica "Guido CASTELNUOVO", Università degli Studi di Roma "La Sapienza", Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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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: Φn(Pn(x)) = Pn-1(x), Ψn(Pn(x)) = Pn+1(x). 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.