A Computer Proof of Turan's Inequality

Manuel Kauers, Stefan Gerhold

Research output: Contribution to journalArticlepeer-review

Abstract

We show how Turan's inequality $P_n(x)^2-P_{n-1}(x)P_{n+1}(x)\geq0$ for Legendre Polynomials and related inequalities can be proven by means of a computer procedure. The use of this procedure simplifies the daily work with inequalities. For instance, we have found the stronger inequality $|x|P_n(x)^2-P_{n-1}(x)P_{n+1}(x)\geq0$ ($-1\leq x\leq 1$) effortlessly with the aid of our method}, journal = {Journal of Inequalities in Pure and Applied Mathematics
Original languageEnglish
Pages (from-to)1-4
Number of pages4
JournalJournal of Inequalities in Pure and Applied Mathematics
Volume7
Issue number2
Publication statusPublished - May 2006

Fields of science

  • 101 Mathematics
  • 101001 Algebra
  • 101005 Computer algebra
  • 101009 Geometry
  • 101012 Combinatorics
  • 101013 Mathematical logic
  • 101020 Technical mathematics

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