@**article**{RISC2876,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}

}