Spans of Polynomials and the Spans of a Laguerre-Polya-Schur Sequence of Polynomials.

摘要

This document proves a conjecture of Meir and Sharma from 1969 determining the least value of the span of a certain derivative P'(x) for > or = 3, if x sub 1 and x sub n are kept fixed. Tools used are the Descartes rule of signs and the inequality > or = H between the arithmetic and harmonic mean. The author also applies his results to the infinite sequences of polynomials introduced by G. Polya and I. Schur in a famous paper from 1914.