03/07/2013, 12:16 AM

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

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