Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))

Linear Mode

Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))

andydude Offline

Long Time Fellow

Posts: 510
Threads: 44
Joined: Aug 2007

#74

12/10/2007, 03:14 AM

@Ivars
What are you talking about? The statement "h(1/x^x) * h(x^1/x) = 1" could be interpreted in at least four ways:

\( h\left(\frac{1}{x^x}\right) h\left(\frac{x^1}{x}\right) = 1 \) (with the usual order of operations), or
\( h\left(\frac{1}{x^x}\right) h\left(x^{(1/x)}\right) = 1 \)
\( h\left((1/x)^x\right) h\left(\frac{x^1}{x}\right) = 1 \)
\( h\left((1/x)^x\right) h\left(x^{(1/x)}\right) = 1 \) (assuming the order of operations of "/" and "^" are opposite from their usual order)

could you please clarify this so I can either agree or disagree with this?

@Gottfried
Also, it took me 3 months to understand your graphs, but I think I understand them now. It seems like you were trying to plot a graph like this:

[Image: selfroot-real-zeros.png]

which is the contour plot of \( \text{Im}(x^{1/x}) = 0 \). However, I still don't understand the questions your asking, which makes it hard to get through this 8-page thread. If someone could summarize the questions and results in this thread, I would be very thankful. Smile

Andrew Robbins

Website Find

« Next Oldest | Next Newest »

Messages In This Thread

Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 09/08/2007, 09:07 AM

RE: The Complex Inverse h of x^(1/x) - by Gottfried - 09/10/2007, 01:59 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 09/11/2007, 12:18 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 09/19/2007, 05:17 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by GFR - 09/21/2007, 02:01 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 09/21/2007, 04:57 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by GFR - 09/21/2007, 05:11 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 09/22/2007, 07:36 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 10/20/2007, 01:49 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 10/30/2007, 06:00 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/02/2007, 08:43 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/03/2007, 12:10 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/03/2007, 12:54 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/03/2007, 03:17 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/03/2007, 08:33 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/03/2007, 09:09 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/07/2007, 12:30 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/03/2007, 10:12 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/04/2007, 12:10 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/04/2007, 12:42 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/04/2007, 02:17 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/04/2007, 02:38 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/04/2007, 04:31 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/04/2007, 05:00 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/04/2007, 10:15 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/04/2007, 10:53 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/05/2007, 05:50 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/06/2007, 01:34 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/06/2007, 10:14 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/07/2007, 12:12 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/07/2007, 10:12 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/07/2007, 11:59 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/07/2007, 12:58 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/07/2007, 01:48 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by andydude - 11/14/2007, 05:38 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/07/2007, 10:03 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/07/2007, 10:26 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/08/2007, 02:31 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/08/2007, 02:51 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/09/2007, 08:30 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/09/2007, 08:43 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/09/2007, 11:51 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/12/2007, 08:23 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/13/2007, 11:01 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/14/2007, 05:04 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/14/2007, 02:10 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/14/2007, 02:14 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/14/2007, 02:49 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/14/2007, 04:52 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/14/2007, 08:57 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/14/2007, 10:10 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/15/2007, 06:16 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/15/2007, 09:40 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/15/2007, 04:15 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/15/2007, 10:45 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/16/2007, 09:09 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/16/2007, 12:06 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/16/2007, 02:02 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/16/2007, 03:17 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/16/2007, 05:28 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/17/2007, 11:01 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/20/2007, 10:11 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/22/2007, 01:01 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/22/2007, 06:29 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/29/2007, 10:37 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 12/09/2007, 03:18 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by andydude - 12/10/2007, 03:14 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 12/10/2007, 07:27 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 12/16/2007, 12:02 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 12/16/2007, 02:22 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 12/16/2007, 05:53 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by andydude - 04/14/2008, 01:01 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 04/14/2008, 10:35 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by andydude - 04/25/2008, 11:25 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 12/10/2007, 07:37 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by andydude - 12/10/2007, 04:11 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by jaydfox - 11/15/2007, 07:21 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/15/2007, 09:44 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 11/22/2007, 10:36 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 12/30/2007, 01:09 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 12/30/2007, 03:37 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 12/30/2007, 05:33 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by andydude - 01/05/2008, 08:00 PM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 01/06/2008, 02:55 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 02/07/2008, 10:49 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 04/28/2008, 08:11 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Ivars - 05/09/2008, 06:32 AM

RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 03/03/2011, 03:16 PM

RE: Tetration below 1 - by Gottfried - 09/09/2007, 07:04 AM

RE: The Complex Lambert-W - by Gottfried - 09/09/2007, 04:54 PM

RE: The Complex Lambert-W - by andydude - 09/10/2007, 06:58 AM

Possibly Related Threads…
Thread		Author	Replies	Views	Last Post
	extending normal tetration to real numbers using product tetration	Alex Zuma 2025	0	935	12/12/2025, 07:49 PM Last Post: Alex Zuma 2025
	my proposed extension of the fast growing hierarchy to real numbers	Alex Zuma 2025	0	1,322	09/28/2025, 07:15 PM Last Post: Alex Zuma 2025
	Behaviour of tetration into the real negatives	Shanghai46	1	6,364	03/24/2025, 12:34 AM Last Post: MphLee
	X-th iteration where x is a real number	Natsugou	1	5,671	10/27/2024, 11:23 PM Last Post: MphLee
	Real and complex tetration	Daniel	13	16,939	04/04/2023, 10:25 AM Last Post: JmsNxn
	Range of complex tetration as real	Daniel	2	4,930	10/22/2022, 08:08 PM Last Post: Shanghai46
	From complex to real tetration	Daniel	3	6,249	10/21/2022, 07:55 PM Last Post: Daniel
	Cost of real tetration	Daniel	1	3,991	09/30/2022, 04:41 PM Last Post: bo198214
	Real Multivalued/Parametrized Iteration Groups	bo198214	11	14,680	09/10/2022, 11:56 AM Last Post: tommy1729
	Constructive real tetration	Daniel	1	3,790	09/01/2022, 05:41 AM Last Post: JmsNxn

View a Printable Version

Users browsing this thread: 1 Guest(s)

Login
Username:
Password:	Lost Password?
	Remember me