Characterization of polynomials and divided difference
type: Item
instance of: scholarly article
title: Characterization of polynomials and divided difference
zbMATH Open document ID: 0852.39005
DOI: 10.1007/BF02837195
author: Prasanna Sahoo
author: Pl. Kannappan
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1996-07-15T00:00:00Z
review text: The authors offer two additional proofs of a result by \textit{J. Schwaiger} [Aequationes Math. 48, No. 2-3, 317-323 (1994; Zbl 0810.39007)] that the \((n-1)\)-st divided difference (with variable spans) of \(f\) is a function of the sum of its \(n\) variables iff \(f\) is a polynomial of degree at most \(n\); and \(g\) is linear. The variables and function values are here in the set of all reals (in Schwaiger's paper they are in any field with sufficiently many elements and with characteristic different from 2).
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 903363
zbMATH Keywords: functional equations
zbMATH Keywords: determinants
zbMATH Keywords: divided difference
zbMATH Keywords: polynomial
reviewed by: János Aczél
MaRDI profile type: Publication
cites work: A Mean Value Property of the Derivative of Quadratic Polynomials-without Mean Values and Derivatives
cites work: A Mean-Value Property of Cubic Polynomials-without Mean Values
cites work: A functional identity characterizing polynomials
cites work: A Property of Quadratic Polynomials
cites work: Q4732833
description: scientific article; zbMATH DE number 903363