Manuel Kauers, Stefan Gerhold,
"A Computer Proof of Turan's Inequality"
, Serie SFB F013 Reports, Nummer 2005-15, SFB, Altenbergerstr. 69, 4040 Linz, 9-2005
Original Titel:
A Computer Proof of Turan's Inequality
Sprache des Titels:
Englisch
Original Kurzfassung:
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.
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