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 Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation Base-Acid Tetration Fellow Posts: 94 Threads: 15 Joined: Apr 2009 10/15/2009, 09:39 PM (This post was last modified: 10/15/2009, 09:52 PM by Base-Acid Tetration.) (10/15/2009, 08:17 AM)andydude Wrote: Tetration isn't entire, it's holomorphic over the complex plane cut along the negative reals < -2.I said PENTation. (10/15/2009, 05:01 PM)bo198214 Wrote: (10/13/2009, 09:47 PM)Base-Acid Tetration Wrote: Theorem. There exists no entire pentation pen_b(z), for b>1, such that pen(0) = 1. Either you have to specify that pen must use the principal branch of tetration (the cut is nothing god given, its just a choice to our human preference; the real function lives on Riemann manifolds), or you have to modify your proof and use the singularities of tetration at integers <=-2 (and show before that indeed every tetration has singularities there). I DID say: BAT Wrote:Let Tet_b(z) be the principal branch of tetration.I fixed the proof to make this clearer. I also did say that if we didn't restrict ourselves to the principal branch an entire pentation may be possible: BAT Wrote:Or alternatively we can incorporate parts of non-prinicipal branches of tetration (analytically continued around z = -2) in our construction of a holomorphic pentation? I meant if it can just avoid -2, pentation can still be entire. Now the question is, is it morally good to restrict ourselves to the principal branch? (BTW, what kind of singularities does Tet have at integers<=-2? Are they all logarithmic-type branch points around which the function winds infinitely many times?) Let's get back to the point. WHERE THE HECK ARE THE COMPLEX FIXED POINTS? « Next Oldest | Next Newest »

 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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