• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Where is the proof of a generalized integral for integer heights? Chenjesu Junior Fellow Posts: 21 Threads: 4 Joined: May 2016 03/03/2019, 06:05 AM (This post was last modified: 03/03/2019, 06:35 AM by Chenjesu.) https://en.wikipedia.org/wiki/List_of_in..._functions Under "other integrals" it gives the integral of any integer height but provides no proof or citation. I remember seeing a paper with similar formula some time ago, but at the end it said something about its conjecture being unproven. Is there any reference that proves this integral formula? Micah Junior Fellow Posts: 9 Threads: 2 Joined: Feb 2019 03/03/2019, 07:29 AM (This post was last modified: 03/03/2019, 07:31 AM by Micah. Edit Reason: found source of interest ) Are we certain that the form posted on Wikipedia is correctly derived?  Without the proof there may be no way of knowing it's correctness, We could take a look at the first few cases of the integral in order to inspect the forms, and then conjecture about a generalization from there, have you derived the first few forms of the integral?  $\int\limits x^x dx = I_1$ $\int\limits x^{x^x} dx = I _2$  $\dots$  That may be a starting point for a proof.  Also, I may be misinterpreting something on the wikipedia page that you posted, but shouldn't there be constants of integration in all of these antiderivatives as they do not have limits?  This may also be of some use: https://en.wikipedia.org/wiki/Puiseux_series Thanks for the thought provoking question!  -Micah Chenjesu Junior Fellow Posts: 21 Threads: 4 Joined: May 2016 03/03/2019, 08:55 AM (This post was last modified: 03/03/2019, 08:57 AM by Chenjesu.) I am not sure it is correct at all, that is why I am asking for the proof. I think it's likely someone found that old paper with the unproven conjecture and stuck it on wikipedia without reading it carefully. « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post Closed Forms for non Integer Tetration Catullus 1 110 07/08/2022, 11:32 AM Last Post: JmsNxn Some "Theorem" on the generalized superfunction Leo.W 48 16,217 06/18/2022, 08:39 AM Last Post: Leo.W Ueda - Extension of tetration to real and complex heights MphLee 4 1,229 05/08/2022, 11:48 PM Last Post: JmsNxn The Generalized Gaussian Method (GGM) tommy1729 2 1,307 10/28/2021, 12:07 PM Last Post: tommy1729 Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 11,939 05/26/2021, 11:55 PM Last Post: MphLee Generalized phi(s,a,b,c) tommy1729 6 3,260 02/08/2021, 12:30 AM Last Post: JmsNxn (almost) proof of TPID 13 fivexthethird 1 5,304 05/06/2016, 04:12 PM Last Post: JmsNxn Tetration series for integer exponent. Can you find the pattern? marraco 20 33,285 02/21/2016, 03:27 PM Last Post: marraco Lit: f(x)=log(x) iff x is integer Gottfried 3 8,906 03/17/2015, 11:35 PM Last Post: tommy1729 Tommy's conjecture : every positive integer is the sum of at most 8 pentatope numbers tommy1729 0 3,961 08/17/2014, 09:01 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)