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Does the exponential function have a square root?(asked by Nathaniel Hellerstein on the Q&A board at JMM) Is there a "half-exponential" function h(x) such that h(h(x))=ex? Is it unique? Is it analytic? Related question: Is there an invertible smooth function E such that E(x+1)=eE(x)? Is it unique? If so, then we can take h(x)=E(E-1(x)+1/2). [Ed: please retag appropriately]
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