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Characterization of polynomials and divided difference
Proceedings of the Indian Academy of Sciences - Section A, 1995For distinct points x1,x2,…,xn in ℛ (the reals), letϕ[x1, x2,…,xn] denote the divided difference ofϕ. In this paper, we determine the general solutionϕ,g: ℛ → ℛ of the functional equationϕ[x1,x2,…,xn] =g(x1,+ x2 + … + xn) for distinct x1,x2,…, xn in ℛ without any regularity assumptions on the unknown functions.
Prasanna K. Sahoo, Pl. Kannappan
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A New Type of Difference Dimension Polynomials
Mathematics and Computer Science, 2022A. Levin
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On the uniqueness of certain types of differential-difference polynomials
Ukrains'kyi Matematychnyi Zhurnal, 2017A. Banerjee, S. Majumder
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On the difference of successive Gaussian polynomials
Journal of Statistical Planning and Inference, 1993Abstract In this paper we provide a partition-theoretic interpretation of the difference of two successive Gaussian polynomials, namely q − j ([ n + j j ] − [ n + j j −1 ]).
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Zero Distribution on Differential-Difference Polynomials of Exponential Type Functions
Computational methods in Function Theory, 2019Kai Liu, Linkui Gao, Xinling Liu
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Further results on certain type of nonlinear difference polynomials
Rendiconti del Circolo Matematico di Palermo Series 2, 2018Maamar Andasmas, Z. Latreuch
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Conversion of Polynomials between Different Polynomial Bases [PDF]
IMA Journal of Numerical Analysis, 1981 Y. L. Luke, B. Y. Ting
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Multivariable Difference Dimension Polynomials
Journal of Mathematical Sciences, 2005Let K be a difference field with basic set of translations σ and let a partition of the set σ into p disjoint subsets be fixed. Let \(\mathcal{D}\) be the ring of difference operators over K treated as a filtered ring with the natural p-dimensional filtration.
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Singular Manifolds of Difference Polynomials
The Annals of Mathematics, 19511. 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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