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  • @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}
    }