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 using sinh(x) ? tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 06/23/2010, 09:31 PM (06/23/2010, 09:11 PM)tommy1729 Wrote: to go towards the taylor series you simply take the derivates you need of $\ln^{[n]} (\2sinh^{[z]}(exp^{[n]}(x)))$ and create the taylor series with real coefficients. then just plug in complex Z instead of x and your done. however the question is , what is the radius of that taylor series expanded at x = 0 or even elsewhere. if that radius is nonzero , we could probably extend further by using analytic continuation , or mittag-leffler expansion. and that is the way we go to the complex plane. perhaps an intresting note is that if the ROC is large , we could check if that taylor series has the same period as exp(x) ( 2pi i ). if it is indeed large enough and 1) the period is indeed 2pi i then the limit formula might hold for the complex plane and be equal to the taylor of the limit formula for the reals. 2) the period is not 2pi i then the limit formula will NOT hold for the complex plane and NOT be equal to the taylor of the limit formula for the reals. also , if the radius is 0 everywhere , despite unlikely , then if the limit converges for all complex , then the function must have some local or global fractal or semi-fractal properties. regards tommy1729 perhaps constructing a fourier series is 'better' , assuming we have the period property of course. 'better ' in the sense of potentially easier to compute numerically , easier to compute 'symbolicly' ( four coeff ) and easier to prove related statements conjectures and properties. this makes me doubt if taylor = four , if the period really exists and if the result only converges for x > 0 ... for reasons not yet explained ... just saying that fourier expansion might be intresting imho. if valid... slightly off topic but i often think there should be a new type of series expansion designed for tetration ... regards tommy1729 « Next Oldest | Next Newest »

 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: attracting fixed point of 2sinh - by tommy1729 - 06/28/2010, 11:23 PM RE: attracting fixed point of 2sinh - by sheldonison - 06/29/2010, 03:18 AM RE: attracting fixed point of 2sinh - by tommy1729 - 06/29/2010, 10:45 PM RE: attracting fixed point of 2sinh - by sheldonison - 06/30/2010, 01:12 AM RE: attracting fixed point of 2sinh - by tommy1729 - 06/30/2010, 02:35 PM RE: attracting fixed point of 2sinh - by sheldonison - 06/30/2010, 03:34 PM 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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