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

Document Type: Research Paper

Author

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

Abstract

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.

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