International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 7, Pages 365-371
Powersum formula for differential resolvents
25 Chestnut Hill Lane, Columbus, NJ 08022-1039, USA
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.
We will prove that we can specialize the indeterminate in a linear differential -resolvent of a univariate polynomial over a differential field of characteristic zero to an integer to obtain a -resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of the -resolvent. Finally, we use the powersum formula to rediscover Cockle's differential resolvent of a cubic trinomial.