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Searching for an asymptotic to exp[0.5]
#59
Im considering that f(f(z)) - exp(z) is small in a region without holes.

The idea of holes fascinates me.

Many conjectures come to my mind though the quality of them is not yet certain.

For instance

CONJECTURE HOLE A
If g(z) is a fake (entire) half-iterate of exp(z) on the positive real line and all the derivatives are positive then g(g(z)) - exp(z) is small in a region without holes.

Problem is also that things are only defined intuitive.
For instance the presence of a hole or not depends on your " definition of small ".
Only depending on your definition of small is if there is 1 hole or 2 holes close together. ( perhaps name that a pseudohole or fake hole ?)

Im not sure if the concept of holes is relevant to the location of zero's of f(z) , some (conjectured) uniqueness conditions , equivalence principles and other stuff discussed sofar , or if it is just a new subject.

Maybe I did to much topology lately.

regards

tommy1729
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Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/26/2014, 12:21 PM

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