@**techreport**{RISC2491,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.},

number = {2005-15},

address = {Altenbergerstrasse 69},

year = {2005},

month = {September},

institution = {SFB F013},

keywords = {Turan's inequality, Cylindrical Algebraic Decomposition},

length = {3}

}