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 Searching for an asymptotic to exp[0.5] sheldonison Long Time Fellow Posts: 641 Threads: 22 Joined: Oct 2008 05/22/2014, 10:16 PM (This post was last modified: 05/23/2014, 04:24 AM by sheldonison.) (05/22/2014, 08:31 AM)tommy1729 Wrote: .... Another " counter-intuitive " (entire) function is this one : $f(z)=\int_0^\infty \frac{e^{zt}}{t^t}\mathrm{d}t$ this entire f(z) is bounded outside the strip $Im(z)=< \pi$. ( this can be shown with contour integration or substitution ) So its almost everywhere constant. .... The fact that a function has no 0 does not limit exp(g(z)) much. So exp(g(z)) can be very different from exp(polynomial). ... On the other hand : if the truncated Taylor series can be approximated well with a truncated product (1+b_n x) then its likely that g(z) is indeed a constant. This is also likely because of the simplification that all derivates are positive and it might be possible to find a recursion to solve for b_n ... So I think truncation and induction will show us the way. Thinking ... regards tommy1729Hey Tommy, Much to learn. I bought Conway's graduate complex analysis book, which includes the Weierstrass factorization theorem. I will add it to my large and growing collection of graduate math books, to supplement my somewhat weak formal math education (BSEE). For the truncated product equation, where z_n are the zeros of the Asymptotic half exponential, is this correct? $(1+b_n x)$ $b_n=\frac{-1}{z_n}$ update I tried Tommy's factor, which works surprisingly well. So I guess this is the Weierstrass factorization of the asymptotic half exponential. $f(z)=\text{half}(0)\times\prod_{n=1}^{\infty}(1-\frac{x}{z_n})$ Here are the first 10 zeros of the asymptotic half exponential. I also have an approximation for the zeros of the asymptotic function, in terms of Kneser's half exponential. Code:1 -0.71176762728441566602682009931906 2 -4.2615192715738731444168590500003 3 -15.214306922947794235707847543680 4 -43.768867332590888558785594556450 5 -109.77901963743164514158613984269 6 -229.50542893029538607241128473700 7 -458.89117411149970236796071783155 8 -861.01099146084982202350824423190 9 -1534.9231313380922901088132019252 10 -2623.2160464901874760015847745797- Sheldon « Next Oldest | Next Newest »

 Messages In This Thread Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/07/2014, 12:22 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/08/2014, 04:25 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/10/2014, 12:14 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/10/2014, 11:31 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/10/2014, 11:48 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/10/2014, 11:58 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/09/2014, 11:19 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/10/2014, 11:56 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/13/2014, 04:23 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/14/2014, 05:54 AM RE: Searching for an asymptotic to exp[0.5] - by JmsNxn - 05/12/2014, 03:48 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/12/2014, 03:56 PM RE: Searching for an asymptotic to exp[0.5] - by JmsNxn - 05/12/2014, 05:06 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/12/2014, 11:35 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/13/2014, 11:44 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/14/2014, 11:42 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/15/2014, 06:15 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/15/2014, 09:49 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/16/2014, 07:27 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/14/2014, 12:20 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 07/17/2014, 05:46 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/15/2014, 08:53 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/16/2014, 09:36 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/16/2014, 10:16 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/18/2014, 06:14 PM RE: Searching for an asymptotic to exp[0.5] - by JmsNxn - 05/22/2014, 12:16 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/22/2014, 07:08 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/22/2014, 08:31 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/22/2014, 10:16 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/23/2014, 10:53 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/25/2014, 03:00 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/29/2014, 11:09 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 07/12/2014, 07:46 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/29/2014, 11:32 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/29/2014, 11:54 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/30/2014, 09:41 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 06/28/2014, 11:16 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/28/2014, 09:52 PM RE: Searching for an asymptotic to exp[0.5] - by JmsNxn - 06/29/2014, 01:40 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 06/30/2014, 12:56 AM RE: Searching for an asymptotic to exp[0.5] - by JmsNxn - 06/30/2014, 03:21 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 06/30/2014, 11:56 PM RE: Searching for an asymptotic to exp[0.5] - by JmsNxn - 07/01/2014, 12:35 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 06/30/2014, 01:27 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/01/2014, 10:10 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 07/01/2014, 11:41 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/02/2014, 09:53 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/10/2014, 11:48 PM RE: Searching for an asymptotic to exp[0.5] - by MorgothV8 - 07/13/2014, 06:48 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/14/2014, 12:27 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/14/2014, 11:16 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/15/2014, 08:22 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/15/2014, 09:43 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/15/2014, 09:48 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/24/2014, 12:10 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/24/2014, 10:47 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 07/25/2014, 02:46 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/24/2014, 10:54 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/26/2014, 12:21 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/27/2014, 08:37 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/27/2014, 05:01 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/28/2014, 12:17 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/28/2014, 10:30 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 07/30/2014, 04:07 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/01/2014, 11:20 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/01/2014, 11:36 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/02/2014, 12:26 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 08/02/2014, 03:44 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/02/2014, 11:02 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/02/2014, 11:48 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 08/03/2014, 04:54 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/03/2014, 08:46 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 08/03/2014, 12:06 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/03/2014, 12:10 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/05/2014, 11:31 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/08/2014, 10:28 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/09/2014, 12:24 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 08/10/2014, 06:08 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/01/2014, 10:24 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/03/2014, 01:04 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/02/2014, 07:46 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/02/2014, 07:53 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/08/2014, 12:56 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/08/2014, 04:15 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/08/2014, 11:03 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/09/2014, 04:33 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/09/2014, 06:26 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/10/2014, 11:02 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/11/2014, 08:02 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/11/2014, 02:13 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/12/2014, 07:49 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/12/2014, 06:35 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/13/2014, 07:15 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/13/2014, 11:25 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/13/2014, 11:45 PM RE: Searching for an asymptotic to exp[0.5] - by jaydfox - 09/13/2014, 11:49 PM RE: Searching for an asymptotic to exp[0.5] - by jaydfox - 09/14/2014, 12:00 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/14/2014, 05:07 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/15/2014, 03:53 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/14/2014, 09:34 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/16/2014, 12:14 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/16/2014, 12:27 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/18/2014, 10:20 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/18/2014, 11:07 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/19/2014, 12:23 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/29/2014, 11:40 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/19/2014, 04:02 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/03/2014, 01:26 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/03/2014, 10:49 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/03/2014, 11:34 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/03/2014, 11:39 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/04/2014, 09:41 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/04/2014, 10:38 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/05/2014, 11:58 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 11/07/2014, 12:27 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 03/28/2015, 11:11 PM RE: Searching for an asymptotic to exp[0.5] - by marraco - 03/29/2015, 12:59 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/25/2015, 10:24 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/25/2015, 10:52 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/15/2015, 06:45 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/15/2015, 06:55 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/17/2015, 01:45 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/18/2015, 09:34 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/18/2015, 09:56 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/18/2015, 10:09 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/31/2015, 04:57 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/31/2015, 05:12 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/15/2015, 10:22 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/16/2015, 02:49 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/16/2015, 03:23 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 08/26/2015, 07:36 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/03/2015, 10:31 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/05/2015, 08:16 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/09/2015, 12:17 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/12/2015, 01:14 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/14/2015, 01:30 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/18/2015, 11:31 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/21/2015, 10:53 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/21/2015, 05:58 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/24/2015, 08:10 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/25/2015, 12:59 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 09/25/2015, 08:26 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/26/2015, 12:24 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/29/2015, 12:28 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 10/01/2015, 07:56 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/30/2015, 12:25 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/30/2015, 09:27 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/01/2015, 11:25 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/02/2015, 02:56 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/03/2015, 10:42 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/06/2015, 12:11 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/06/2015, 12:26 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/08/2015, 07:52 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/08/2015, 12:26 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/08/2015, 10:43 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/08/2015, 11:08 PM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 10/09/2015, 08:15 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/09/2015, 11:56 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 10/10/2015, 03:08 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/10/2015, 07:40 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/08/2015, 11:12 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/09/2015, 07:18 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/10/2015, 08:15 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/10/2015, 08:26 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/11/2015, 07:17 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/17/2015, 11:59 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/18/2015, 11:07 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/18/2015, 11:22 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/19/2015, 12:20 AM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 10/27/2015, 01:27 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 02/16/2016, 03:17 AM RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 02/18/2016, 06:51 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 02/17/2016, 01:25 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 02/18/2016, 12:53 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 02/18/2016, 01:11 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 02/23/2016, 01:01 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 02/23/2016, 01:23 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 03/21/2016, 01:26 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 04/05/2016, 01:29 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/04/2016, 07:21 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/04/2016, 08:16 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/04/2016, 08:29 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/06/2016, 03:12 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/06/2016, 03:47 PM RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 03/15/2018, 01:23 PM

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