$\cos(\cos(\cdots(\cos(x))\cdots))$

Asked Feb 10 '18 at 12:33

Active Mar 09 '18 at 15:15

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$\forall n\in \mathbb N$, Let $$f_n (x)=\underbrace{\cos(\cos(\cos(\cdots (\cos}_n(x\underbrace{))\cdots)}_n$$ It is known that $$\forall x\in\mathbb R,\space \lim_{n\rightarrow\infty}f_n(x)=0.7390851332\dots$$Does the convergence uniform?

edited Mar 09 '18 at 15:15

TheSimpliFire

28,020

asked Feb 10 '18 at 12:33

Tony Ma

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This question has been asked and answered several times in the past. See (1), (2), and (3) for examples. I'm personally rather fond of the version of the question to which I linked above, though I am biased in that regard. – Xander Henderson Feb 10 '18 at 12:40

$\cos(\cos(\cdots(\cos(x))\cdots))$

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