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A Computer Proof of Turan's Inequality
[article]
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