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 Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 10/23/2009, 08:01 PM (This post was last modified: 10/23/2009, 08:11 PM by andydude.) Ok, I think I know what you were talking about now. The primary branchpoints of pentation are going to be where you see the logarithmic singularities in the picture below. These are approximately at $-1.68187 \pm 1.33724 I$ which is also approximately ${}^{\infty}e - 2$. It is not exact, because the region between -1 and 0 is only approximately (x+1). In other words, if L is a branchpoint of the superlogarithm, then $slog(slog(L))$ is going to be branchpoint of pentation. I also plotted two branch systems: A, from branchpoints to imaginary infinities D, from branchpoints to negative infinity The function being plotted is actually: $f(z) = \begin{cases} \text{slog}(f(z + 1)) & \text{if } Re(z) < 0 \\ {}^{z}e & \text{if } 0 \le Re(z) \le 1 \\ \text{sexp}(f(z - 1)) & \text{if } Re(z) > 1 \end{cases}$ Andrew Robbins Attached Files Image(s) « 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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