A Computer Proof of Turán’s Inequality
نویسندگان
چکیده
We show how Turán’s inequality Pn(x) −Pn−1(x)Pn+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|Pn(x) 2 − Pn−1(x)Pn+1(x) ≥ 0, −1 ≤ x ≤ 1, effortlessly with the aid of our method.
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