Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation

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Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation

bo198214 Offline

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#12

10/17/2009, 04:37 PM

(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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Messages In This Thread

Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/13/2009, 03:53 AM

RE: complex fixed points of tetration/tetralogarithm - by bo198214 - 10/13/2009, 07:45 AM

RE: complex fixed points of tetration/tetralogarithm - by Base-Acid Tetration - 10/13/2009, 07:46 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/13/2009, 09:47 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/15/2009, 08:17 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/15/2009, 05:01 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/15/2009, 09:39 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/16/2009, 06:28 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/16/2009, 08:52 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/17/2009, 10:47 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/17/2009, 04:37 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/17/2009, 08:23 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/17/2009, 02:59 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/17/2009, 09:29 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/23/2009, 08:01 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/23/2009, 09:03 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/23/2009, 09:27 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/24/2009, 12:26 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/24/2009, 12:31 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/24/2009, 04:12 AM

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