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Results tagged with ca.classical-analysis-and-odes
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user 396106
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Behavior of $n^\alpha \sin^{\circ\, n}(n^{-\alpha}x)$
I'll write it formally: Let $\sin^{\circ\, 1}(x) = \sin(x)$ and $\sin^{\circ n+1}(x) = \sin\bigl(\sin^{\circ n}(x)\bigr)$ for $n\in \Bbb N$ with $n>1$.
What is the limit as $n \to \infty$?
It's fairly …