The algebra of factorial polynomials
D. Babusci, G. Dattoli, M. Carpanese
TL;DR
This paper explores the formal properties of factorial polynomials and their series, developing a theoretical framework using quasi-monomials to solve complex difference equations.
Contribution
It introduces a new formalism for factorial polynomials and demonstrates its effectiveness in solving nontrivial difference equations.
Findings
Developed a formal theory of factorial polynomials
Proved the utility of quasi-monomials in difference equations
Provided methods for solving complex difference equations
Abstract
We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of the method for the solutions of nontrivial difference equations.
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Taxonomy
TopicsPolynomial and algebraic computation · Functional Equations Stability Results · Advanced Differential Equations and Dynamical Systems