author = {Stefan Gerhold and Manuel Kauers},
title = {{A Computer Proof of Turan's Inequality}},
language = {english},
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},
volume = {7},
number = {2},
pages = {1--4},
isbn_issn = {?},
year = {2006},
month = {May},
note = {Article 42},
refereed = {yes},
length = {4}