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Is the half iterate of 2sinh(x) analytic near R ?
#1
Is the half iterate of 2sinh(x) - expanded from fixpoint 0 - analytic near R ?
And does it satisfy its functional equation ( composition towards 2sinh(x) ) wherever it is analytic ( near R ) ?

I know the taylor series is messed up because we have 2 complex conjugate fixpoints.

However a taylor series can converge outside its radius.

This might be a general idea that we need a general tool for.

regards

tommy1729
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#2
Does the taylor series expanded from 0 converge outside its radius ?
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