What is the power series of a half-exponential function?
Half-exponential means that $f(f(x)) = y^x, y > 1$
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This appears closely related to two earlier questions regarding the half-iterates of [$e^x$](http://math.stackexchange.com/questions/65876/) and [$2^x$](http://math.stackexchange.com/questions/868591/). – Semiclassical Jul 21 '14 at 05:14
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what is $\Theta$? If you just mean $f(f(x))$ remains within a bounded factor of $y^x$ I don't see why there should be _one_ power series. If you mean $f(f(x))=y^x$ you can get the first few terms of the series by expanding and equating coefficients. – Silvio Levy Jul 21 '14 at 05:24
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@SilvioLevy deleted the unnecessary big-theta – Demi Jul 21 '14 at 05:41