On the $s^{th}$ derivative of a polynomial

Document Type : Research Paper


Department of Mathematics, University of Kashmir, Srinagar, $190006$, (India)


For every $1\leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.


Volume 7, Issue 1 - Serial Number 1
January 2016
Pages 141-145
  • Receive Date: 24 October 2013
  • Revise Date: 11 December 2014
  • Accept Date: 17 July 2015
  • First Publish Date: 01 January 2016