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using sinh(x) ?
#55
as said before exp exp exp ... (z) does *not converge* in a neighbourhood of z when im(z) =/= 0.

i believe my algoritm is coo on the reals and by analytic continuation / mittag leffler expansion we can construct " the " (imho i.e. "my") sexp.

by * not converge* i mean it is chaotic , since of course exp exp ... (2) also diverges.

this is so because e^(x + yi) = e^x ( cos y + sin y i ) and large y can become arbitrary close to a multiple of 2pi.

although analytic continuation solves the problem - assuming it works and it has period 2pi i - i would like to investigate further the behaviour of the exp iteration.

for instance , is it true that the neighbourhood of z always contains exactly one non-chaotic value ? call it hp.

assuming we can find hp for every z as a limiting sequence going to zero in the correct way.

is it then possible to extend my formula to :

exp^[z1,z] = ln ln ln ... 2sinh^[z] exp exp exp ... ( z1 + hp(z1) )


regards

tommy1729
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Messages In This Thread
using sinh(x) ? - by tommy1729 - 02/28/2010, 12:22 AM
RE: using sinh(x) ? - by tommy1729 - 03/06/2010, 12:35 PM
RE: using sinh(x) ? - by bo198214 - 03/07/2010, 11:19 AM
using 2* sinh(x) ! - by tommy1729 - 03/09/2010, 01:31 PM
RE: using 2* sinh(x) ! - by bo198214 - 03/10/2010, 11:38 AM
RE: using 2* sinh(x) ! - by tommy1729 - 03/11/2010, 12:50 AM
RE: using 2* sinh(x) ! - by tommy1729 - 03/14/2010, 01:07 AM
RE: using 2* sinh(x) ! - by sheldonison - 06/02/2010, 04:47 PM
RE: using 2* sinh(x) ! - by tommy1729 - 06/02/2010, 10:13 PM
RE: using 2* sinh(x) ! - by sheldonison - 06/02/2010, 10:56 PM
RE: using 2* sinh(x) ! - by tommy1729 - 06/07/2010, 12:34 AM
RE: using 2* sinh(x) ! - by sheldonison - 06/08/2010, 01:59 PM
RE: using 2* sinh(x) ! - by tommy1729 - 06/09/2010, 12:18 PM
RE: using 2* sinh(x) ! - by mike3 - 06/11/2010, 02:23 AM
RE: using 2* sinh(x) ! - by bo198214 - 06/12/2010, 04:36 AM
RE: using 2* sinh(x) ! - by mike3 - 06/12/2010, 11:14 AM
RE: using 2* sinh(x) ! - by tommy1729 - 06/21/2010, 09:14 PM
RE: using 2* sinh(x) ! - by sheldonison - 06/23/2010, 06:06 PM
RE: using 2* sinh(x) ! - by tommy1729 - 06/23/2010, 09:11 PM
RE: using 2* sinh(x) ! - by tommy1729 - 06/23/2010, 09:31 PM
RE: using 2* sinh(x) ! - by bo198214 - 06/27/2010, 09:16 AM
RE: using 2* sinh(x) ! - by sheldonison - 06/04/2010, 04:48 AM
RE: using sinh(x) ? - by tommy1729 - 04/24/2010, 11:47 PM
RE: using sinh(x) ? - by bo198214 - 05/31/2010, 05:52 AM
RE: using sinh(x) ? - by tommy1729 - 06/01/2010, 10:58 PM
RE: using sinh(x) ? - by bo198214 - 06/02/2010, 02:58 AM
RE: using sinh(x) ? - by tommy1729 - 06/22/2010, 11:18 PM
RE: using sinh(x) ? - by tommy1729 - 06/23/2010, 10:44 PM
RE: using sinh(x) ? - by tommy1729 - 06/24/2010, 12:29 PM
RE: using sinh(x) ? - by tommy1729 - 06/24/2010, 07:22 PM
RE: using sinh(x) ? - by bo198214 - 06/26/2010, 12:04 PM
RE: using sinh(x) ? - by tommy1729 - 06/26/2010, 09:19 PM
attracting fixed point of 2sinh - by sheldonison - 06/27/2010, 03:31 AM
RE: using sinh(x) ? - by tommy1729 - 07/18/2010, 10:41 PM
RE: using sinh(x) ? - by sheldonison - 07/19/2010, 09:37 PM
RE: using sinh(x) ? - by tommy1729 - 07/20/2010, 08:24 PM
RE: using sinh(x) ? - by tommy1729 - 07/19/2010, 10:20 PM
RE: using sinh(x) ? - by sheldonison - 07/20/2010, 03:13 PM
RE: using sinh(x) ? - by tommy1729 - 07/20/2010, 08:31 PM
RE: using sinh(x) ? - by sheldonison - 07/21/2010, 03:19 AM
RE: using sinh(x) ? - by tommy1729 - 07/21/2010, 10:34 PM
RE: using sinh(x) ? - by sheldonison - 07/22/2010, 12:23 PM
RE: using sinh(x) ? - by tommy1729 - 07/28/2010, 02:24 PM
RE: using sinh(x) ? - by tommy1729 - 07/28/2010, 02:53 PM
RE: using sinh(x) ? - by tommy1729 - 12/04/2010, 11:09 PM
RE: using sinh(x) ? - by tommy1729 - 12/08/2010, 02:31 PM
RE: using sinh(x) ? - by sheldonison - 01/17/2011, 07:43 PM
RE: using sinh(x) ? - by tommy1729 - 01/17/2011, 11:36 PM
RE: using sinh(x) ? - by tommy1729 - 07/02/2011, 10:32 PM
RE: using sinh(x) ? - by tommy1729 - 07/04/2011, 10:56 PM
RE: using sinh(x) ? - by sheldonison - 07/05/2011, 01:09 AM
RE: using sinh(x) ? - by tommy1729 - 07/05/2011, 12:06 PM
RE: using sinh(x) ? - by tommy1729 - 11/18/2012, 11:41 PM
RE: using sinh(x) ? - by sheldonison - 11/20/2012, 12:01 AM
RE: using sinh(x) ? - by tommy1729 - 11/20/2012, 10:53 PM
RE: using sinh(x) ? - by sheldonison - 11/20/2012, 11:01 PM
RE: using sinh(x) ? - by tommy1729 - 11/20/2012, 11:32 PM
RE: using sinh(x) ? - by sheldonison - 11/20/2012, 11:46 PM
RE: using sinh(x) ? - by tommy1729 - 11/28/2012, 06:59 PM
RE: using sinh(x) ? - by tommy1729 - 11/28/2012, 08:07 PM
RE: using sinh(x) ? - by tommy1729 - 12/17/2012, 04:34 PM
RE: using sinh(x) ? - by tommy1729 - 02/10/2015, 12:02 AM
RE: using sinh(x) ? - by tommy1729 - 04/22/2015, 12:27 PM
RE: using sinh(x) ? - by tommy1729 - 04/23/2015, 04:49 PM
RE: using sinh(x) ? - by tommy1729 - 10/26/2015, 12:56 AM
RE: using sinh(x) ? - by tommy1729 - 11/26/2015, 11:56 PM
RE: using sinh(x) ? - by sheldonison - 11/27/2015, 03:41 PM
RE: using sinh(x) ? - by tommy1729 - 11/28/2015, 01:21 PM
RE: using sinh(x) ? - by sheldonison - 11/29/2015, 03:03 PM
RE: using sinh(x) ? - by tommy1729 - 12/01/2015, 01:22 PM
RE: using sinh(x) ? - by sheldonison - 12/01/2015, 02:58 PM
RE: using sinh(x) ? - by tommy1729 - 12/02/2015, 12:04 AM
RE: using sinh(x) ? - by tommy1729 - 12/01/2015, 08:18 PM
RE: using sinh(x) ? - by tommy1729 - 12/02/2015, 12:28 AM
RE: using sinh(x) ? - by tommy1729 - 02/23/2016, 10:36 PM
RE: using sinh(x) ? - by tommy1729 - 02/24/2016, 01:27 PM
RE: using sinh(x) ? - by tommy1729 - 03/01/2016, 10:38 PM
RE: using sinh(x) ? - by tommy1729 - 03/05/2016, 01:27 PM
RE: using sinh(x) ? - by tommy1729 - 03/05/2016, 11:38 PM
RE: using sinh(x) ? - by sheldonison - 03/06/2016, 03:16 PM
RE: using sinh(x) ? - by tommy1729 - 03/06/2016, 10:54 PM
RE: using sinh(x) ? - by tommy1729 - 03/07/2016, 01:48 AM
RE: using sinh(x) ? - by tommy1729 - 03/07/2016, 10:46 AM
RE: using sinh(x) ? - by tommy1729 - 03/07/2016, 09:36 PM
RE: using sinh(x) ? - by tommy1729 - 03/08/2016, 12:26 AM
RE: using sinh(x) ? - by tommy1729 - 03/11/2016, 01:27 PM
RE: using sinh(x) ? - by tommy1729 - 03/12/2016, 01:12 PM
RE: using sinh(x) ? - by tommy1729 - 03/12/2016, 01:20 PM

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