RISC RISC Research Institute for Symbolic Computation  
  • @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}