Powersum formula for polynomials whose distinct roots are differentially independent over constants
type: Item
instance of: scholarly article
title: Powersum formula for polynomials whose distinct roots are differentially independent over constants
zbMATH Open document ID: 1021.12005
DOI: 10.1155/S0161171202202331
author: John Michael Nahay
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/50317
review text: Summary: We prove that the author's powersum formula yields a nonzero expression for a particular linear ordinary differential equation, called a resolvent, associated with a univariate polynomial whose coefficients lie in a differential field of characteristic zero provided the distinct roots of the polynomial are differentially independent over constants. By definition, the terms of a resolvent lie in the differential field generated by the coefficients of the polynomial, and each of the roots of the polynomial are solutions of the resolvent. One example shows how the powersum formula works. Another example shows how the proof that the formula is not zero works.
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 13N15
zbMATH DE Number: 1883652
zbMATH Keywords: powersum formula
zbMATH Keywords: resolvent
zbMATH Keywords: differential field of characteristic zero
MaRDI profile type: Publication
OpenAlex ID: W2054205483
description: scientific article; zbMATH DE number 1883652