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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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An Elementary Inequality [closed]
A friend of mine found in the internet the following exercise:
Let $a, b, c \geq 0$ with $a + b + c = 1$. Show that
$$
\sqrt{a + b^2} + \sqrt{b + c^2} + \sqrt{c + a^2} \geq 2,
$$
where equality is att …