• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 Could be tetration if this integral converges tommy1729 Ultimate Fellow Posts: 1,645 Threads: 369 Joined: Feb 2009 05/11/2014, 04:26 PM (This post was last modified: 05/11/2014, 04:29 PM by tommy1729.) (05/03/2014, 01:19 AM)mike3 Wrote: JmsNxn, I am a little suspicious of this method. In particular, I'm not sure the integral $I = \int_{0}^{\infty} \vartheta(-x) x^{z-1} dx$, $0 < z < 1$ converges. I totally agree. Although I added a minus sign to it, which I assume was a typo. So lets think about $\vartheta(-x)$. Since the Taylor coefficients of $\vartheta(-x)$ decay EXTREMELY FAST , I consider this as a function that is well approximated by a polynomial for a long time. ( many remainder theorems for Taylor series imply this ) This means the main behaviour of this $\vartheta(-x)$ is like $(-1)^n a_n x^n$ where n increases slowly with x. This implies that $\vartheta(-x)$ is not bounded by a polynomial and also that $\vartheta(-x)$ = 0 infinitely often. Therefore the integral diverges. Even if we consider taking the limit of x going to +oo as the limit of the sequence x_i with $\vartheta(-x_i)$ = 0. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Could be tetration if this integral converges - by JmsNxn - 04/03/2014, 02:14 PM RE: Could be tetration if this integral converges - by sheldonison - 04/30/2014, 11:17 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/02/2014, 03:33 PM RE: Could be tetration if this integral converges - by tommy1729 - 04/30/2014, 12:29 PM RE: Could be tetration if this integral converges - by mike3 - 05/03/2014, 01:19 AM RE: Could be tetration if this integral converges - by tommy1729 - 05/11/2014, 04:26 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/11/2014, 04:30 PM RE: Could be tetration if this integral converges - by tommy1729 - 05/11/2014, 04:52 PM RE: Could be tetration if this integral converges - by mike3 - 05/03/2014, 05:24 AM RE: Could be tetration if this integral converges - by mike3 - 05/03/2014, 07:13 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/03/2014, 06:12 PM RE: Could be tetration if this integral converges - by mike3 - 05/04/2014, 02:18 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/04/2014, 07:27 PM RE: Could be tetration if this integral converges - by mike3 - 05/05/2014, 12:55 AM RE: Could be tetration if this integral converges - by mike3 - 05/04/2014, 11:50 AM RE: Could be tetration if this integral converges - by sheldonison - 05/04/2014, 03:28 PM RE: Could be tetration if this integral converges - by mike3 - 05/05/2014, 01:00 AM RE: Could be tetration if this integral converges - by sheldonison - 05/05/2014, 03:49 PM RE: Could be tetration if this integral converges - by tommy1729 - 05/04/2014, 01:25 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/04/2014, 07:36 PM RE: Could be tetration if this integral converges - by MphLee - 05/04/2014, 07:44 PM RE: Could be tetration if this integral converges - by mike3 - 05/04/2014, 10:42 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/04/2014, 11:32 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/04/2014, 09:06 PM RE: Could be tetration if this integral converges - by mike3 - 05/05/2014, 02:11 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/05/2014, 04:27 PM RE: Could be tetration if this integral converges - by mike3 - 05/05/2014, 11:45 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/06/2014, 12:11 AM RE: Could be tetration if this integral converges - by mike3 - 05/06/2014, 06:50 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/06/2014, 03:54 PM RE: Could be tetration if this integral converges - by mike3 - 05/07/2014, 03:25 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/07/2014, 03:18 PM RE: Could be tetration if this integral converges - by mike3 - 05/11/2014, 07:47 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/11/2014, 04:29 PM RE: Could be tetration if this integral converges - by mike3 - 05/11/2014, 11:26 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/12/2014, 01:44 AM RE: Could be tetration if this integral converges - by mike3 - 05/12/2014, 02:15 AM RE: Could be tetration if this integral converges - by JmsNxn - 05/12/2014, 03:32 PM RE: Could be tetration if this integral converges - by tommy1729 - 05/12/2014, 11:26 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/13/2014, 01:58 PM RE: Could be tetration if this integral converges - by JmsNxn - 05/05/2014, 06:18 PM RE: Could be tetration if this integral converges - by tommy1729 - 05/05/2014, 09:09 PM

 Possibly Related Threads… Thread Author Replies Views Last Post Where is the proof of a generalized integral for integer heights? Chenjesu 2 4,960 03/03/2019, 08:55 AM Last Post: Chenjesu [integral] How to integrate a fourier series ? tommy1729 1 5,265 05/04/2014, 03:19 PM Last Post: tommy1729 Some integral transforms related to tetration JmsNxn 0 3,536 05/02/2013, 07:54 PM Last Post: JmsNxn (draft) integral idea tommy1729 0 4,233 06/25/2011, 10:17 PM Last Post: tommy1729 Cauchy integral also for b< e^(1/e)? bo198214 14 25,061 04/24/2009, 05:29 PM Last Post: bo198214

Users browsing this thread: 1 Guest(s)