JIPAM

A Computer Proof of Turán's Inequality  
 
  Authors: Stefan Gerhold, Manuel Kauers,  
  Keywords: Turán's inequality, Cylindrical Algebraic Decomposition.  
  Date Received: 20/09/05  
  Date Accepted: 10/03/06  
  Subject Codes:

26D07, 33C45, 33F10.

  
  Editors: Doru Stefanescu,  
 
  Abstract:

We show how Turán's inequality $P_n(x)^2-P_{n-1}(x)P_{n+1}(x)geq 0$ 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 $ vert xvert P_n(x)^2-P_{n-1}(x)P_{n+1}(x)geq 0$, $-1leq xleq 1$, effortlessly with the aid of our method.;


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