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## Is there any solution to this kind of equation? Or any clue to explore it? [closed]

Possible Duplicate:
How to solve f(f(x)) = cos(x) ?

$f(f(x))=sin x$

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 See mathoverflow.net/questions/17605/… – Daniel Moskovich Jun 13 2012 at 9:22 Your question differs from the title of the other question, but the body of the other question is sufficiently general to cover your case. – S. Carnahan♦ Jun 13 2012 at 9:39

## closed as exact duplicate by David Roberts, S. Carnahan♦Jun 13 2012 at 9:38

$f(f(x)) = \frac{1}{2} ie^{-i x}-\frac{1}{2} i e^{ix}$