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

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1984
Accession Number
ADA149384

Entities

People

  • Isaac Jacob Schoenberg

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Arithmetic
  • Classification
  • Contracts
  • Equations
  • Identities
  • Inequalities
  • Mathematical Analysis
  • Mathematics
  • Notation
  • Numbers
  • Numerical Analysis
  • Polynomials
  • Sequences
  • Square Roots
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.