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Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation
#12
(10/17/2009, 10:47 AM)andydude Wrote: It is well known that there is a logarithmic singularity at -2, which is a specific kind of essential singularity.

A logarithmic singularity is not an essential singularity!
All 3 types: removable singularity, pole and essential singularity, are isolated singularities, i.e. the function is holomorphic in vicinity except at that singularity.
This is not the case for the logarithm at 0.
0 is a branchpoint of the logarithm and of roots.

Quote:It is also known that there are essential singularities at -3, -4, etc, but exactly what kind of singularities these are is not well known.

Jay would call them doubly, trice, etc logarithmic. These all are branchpoints not isolated singularities.
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RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/17/2009, 04:37 PM

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