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On an inequality

Real & Complex Analysis, Calculus & Multivariate Calculus, Functional Analysis,
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Riemann
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On an inequality

#1

Post by Riemann » Tue Oct 25, 2016 6:45 pm

Define $\displaystyle \Omega(t) = \int_{0}^{1} \frac{1-x^2}{1+tx^2 + x^4} \, {\rm d}x$ and consider the numbers $a,b, c>2$. Prove that:

$$2a b \Omega(c) +2 b c \Omega(a) + 2 ca \Omega(b) < a^2 + b^2 + c^2 $$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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