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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Conditions under which inequality holds for all triplets of non-negative reals
I have the following inequality:
$$ \left(\frac{1}{3}
\left(
\left(\frac{a+b}{2}\right)^3 +
\left(\frac{a+c}{2}\right)^3 +
\left(\frac{b+c}{2}\right)^3 \right) \right)^\frac{1} …