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The Properties of Differential-Difference Polynomials

Ukrainian Mathematical Journal, 2017
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Kai Liu, T. Cao, Xinling Liu
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Difference polynomials and their generalizations

Mathematika, 2001
\textit{A. Ehrenfeucht} [Pr. Mat. 2, 167--169 (1956; Zbl 0074.25505)] proved that a difference polynomial \(f(X)-g(Y)\) in two variables \(X,Y\) with complex coefficients is irreducible provided that the degrees of \(f\) and \(g\) are coprime. \textit{G. Angermüller} [A generalization of Ehrenfeucht's irreducibility criterion. J.
Bhatia, Saurabh, Khanduja, Sudesh K.
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Multivariable Difference Dimension Polynomials

Journal of Mathematical Sciences, 2005
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Remarks on Difference-Polynomials

Bulletin of the London Mathematical Society, 1985
A polynomial of the form \(f(x)-g(y),\) where x and y are disjoint finite sets of variables, is called a difference polynomial. Let \(P(x)-Q(y)\) and \(P^*(x)-Q^*(y)\) be two difference-polynomials having an irreducible common factor F. The main theorem of this article establishes the existence of a difference polynomial f(x)-g(y) which is divisible by
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Polynomials and divided differences

Publicationes Mathematicae Debrecen, 2005
\textit{J. Aczél} showed in 1963 [see Math. Mag. 58, 42--45 (1985; Zbl 0571.39005)] that there is a simple functional equation involving two unknown functions, say \(f\) and \(g\), whose general solution (no regularity conditions whatever) is: \(f\) is a polynomial of degree at most 2 and \(g\) is the derivative of \(f\).
Riedel, Thomas, Sablik, Maciej, Sklar, Abe   +2 more
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Finite Differences and Orthogonal Polynomials

The Ramanujan Journal, 1999
By combining finite differences with symmetric functions, we present an elementary demonstration for the limit relation from Laguerre to Hermite polynomials, proposed by Richard Askey. Another limit relation between these two polynomials is also established.
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Singular Manifolds of Difference Polynomials

The Annals of Mathematics, 1951
1. Let F be an algebraically irreducible difference polynomial in unknowns Y1, Y2, ... , yn with coefficients in a difference field W. We showed previously' that the irreducible components of the manifold of F are of two types: ordinary manifolds not held by any polynomial of lower effective order than F in any yj; and essential singular manifolds ...
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Uniqueness of meromorphic functions sharing sets with its linear difference polynomials

The Journal of Analysis, 2022
Goutam Haldar
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The class of meromorphic functions sharing values with their difference polynomials

Indian journal of pure and applied mathematics, 2022
M. B. Ahamed
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