A Computer Proof of Turan's Inequality

2005/09/21 by Stefan Gerhold, S. Gerhold, Manuel Kauers +3 · 1 citation
Computer Science · Mathematics · #26D07 #33C45 #33F10 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Mathematics and Applications #Polynomial and algebraic computation #math.CA #math.CO #msc:26D07 #msc:33C45 #msc:33F10

paper · pdf · doi:10.48550/arxiv.math/0509468

arxiv created 2005/09/21 · openalex publication_date 2005/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how Turan's inequality P_n(x)²-P_n-1(x)P_n+1(x)≥ 0 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)≥ 0, -1≤ x≤ 1, effortlessly with the aid of our method.

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