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International Journal of Mathematics and Mathematical Sciences - Volume 32 2002, Issue 12, Pages 721-738

25 Chestnut Hill Lane, Columbus, NJ 08022-1039, USA

Received 20 February 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that the author-s powersum formula yields anonzero expression for a particular linear ordinary differentialequation, called a resolvent, associated with aunivariate polynomial whose coefficients lie in a differentialfield of characteristic zero provided the distinct roots of thepolynomial are differentially independent over constants. Bydefinition, the terms of a resolvent lie in the differential fieldgenerated by the coefficients of the polynomial, and each of theroots of the polynomial are solutions of the resolvent. Oneexample shows how the powersum formula works. Another exampleshows how the proof that the formula is not zero works.





Author: John Michael Nahay

Source: https://www.hindawi.com/



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