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

Thread Rating:

1 Vote(s) - 3 Average
1
2
3
4
5

Thread Modes

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

andydude $Offline$
Long Time Fellow

Posts: 509
Threads: 44
Joined: Aug 2007

#87

04/14/2008, 01:01 AM

I just thought I'd add something I found recently.

A cardioid is a shape that is very similar to this, and I thought I'd try and approximate it. It turns out its not a cardioid, but its very close, and can be approximated with the parametric equations:

$x(t) = a \cos(t) (1+\cos(ct))$
$y(t) = a \sin(t) (1+\cos(ct))$

where a = 1.36 and c = 1.17

Andrew Robbins

Attached Files Image(s)

Filename: selfroot-zeros-approx.png Size: 43.04 KB Less than 1 minute ago

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
	Constructing real tetration solutions	Daniel	4	208	12/24/2019, 12:10 AM Last Post: sheldonison
	Complex or Real numbers more important?	Daniel	0	75	12/22/2019, 10:36 AM Last Post: Daniel
	b^b^x with base 0<b<e^-e have three real fixpoints	Gottfried	1	2,339	11/07/2017, 11:06 AM Last Post: sheldonison
	2 real fixpoints again .......	tommy1729	10	9,271	02/23/2016, 10:17 PM Last Post: tommy1729
	A new set of numbers is necessary to extend tetration to real exponents.	marraco	7	9,304	03/19/2015, 10:45 PM Last Post: marraco
	Real-analytic tetration uniqueness criterion?	mike3	25	21,422	06/15/2014, 10:17 PM Last Post: tommy1729
	About real limits	tommy1729	1	2,419	09/23/2013, 09:24 PM Last Post: tommy1729
	Solutions to f ' (x) = f(f(x)) ?	tommy1729	1	2,312	08/12/2013, 12:10 AM Last Post: tommy1729
	Real and complex behaviour of the base change function (was: The "cheta" function)	bo198214	39	52,020	08/13/2011, 06:33 PM Last Post: bo198214
	The imaginary tetration unit? ssroot of -1	JmsNxn	2	5,422	07/15/2011, 05:12 PM Last Post: JmsNxn

View a Printable Version

Users browsing this thread: 1 Guest(s)

Login
Username:
Password:	Lost Password?
	Remember me