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Full Version: period of exp exp exp ...
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let exp exp exp ... (z) diverge on the riemann sphere.

then it must enter a cycle.

for every such z , exp(z) = exp^^y (z) for some positive real y.

y is now a function of e^z.

f(e^z) = y.

find/investigate f(e^z).

since z is complex and y is positive real , f(e^z) is not analytic.