A Computer Proof of Turan's Inequality [article]

S. Gerhold, M. Kauers
2005 arXiv   pre-print
We show how Turan's inequality P_n(x)^2-P_n-1(x)P_n+1(x)≥ 0 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)≥ 0, -1≤ x≤ 1, effortlessly with the aid of our method.
arXiv:math/0509468v1 fatcat:77oyhnqrxnhszatoseqttkopza