A Computer Proof of Turan's Inequality
Abstract
We show how Turan's inequality Pn(x)2-Pn-1(x)Pn+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|Pn(x)2-Pn-1(x)Pn+1(x)≥ 0, -1≤ x≤ 1, effortlessly with the aid of our method.
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