International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 5-8, Pages 365-371
doi:10.1155/S0161171204210602

Powersum formula for differential resolvents

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.