Is there any formula for example saying $f^{\frac{1}{2}}(x)$ or $f^{\pi}(x)$? I tried to derive it but couldn't get anywhere.
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There are many ways to define something like applying it half a time, even in the "simple" case of 2×2 matrices. So you probably need more context to make a relevant choice. – Mark S. Mar 11 '22 at 13:36
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No - not in general. But there are cases where this makes some kind of sense – Henry Mar 11 '22 at 13:37