International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 7, Pages 365-371
doi:10.1155/S0161171204210602
Powersum formula for differential resolvents
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Received 5 October 2002
Copyright © 2004 John Michael Nahay. 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 will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q-resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of the α-resolvent. Finally, we use the powersum formula to rediscover Cockle's differential resolvent of a cubic trinomial.