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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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Prove/disprove $(\int_{0}^{2 \pi} \!\!\cos f(x) d x)^{2}+(\int_{0}^{2 \pi}\!\!\! \sqrt{(f'(x...

Don't trust me on this because I have never done calculus of variations (I'm still in high school), but I'm doing this just because I was bored. I also don't know how to insert special characters like …
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