On the Spans of Polynomials and the Spans of a Laguerre-Polya-Schur Sequence of Polynomials.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This document proves a conjecture of Meir and Sharma from 1969 determining the least value of the span of a certain derivative Px 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.
- Theoretical Mathematics