• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Funny method of extending tetration? mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 11/01/2010, 08:32 PM Hi. Does this lead anywhere, or does it just fail? Take the partial sums of $\exp$, a function called the "exponential sum function": $e_n(x) = \sum_{i=0}^{n} \frac{x^i}{i!}$. If we take this at odd values of $n$, there will be a real fixed point. Take the regular iteration at this real fixed point, shifted so that it equals 1 at 0, call it $\mathrm{reg}_{\mathrm{RFP}}[e_n^x](1)$, that is, regular iteration developed at the real fixed point, iterating "1" (i.e. offset so it equals 1 at 0). Now, what does $\lim_{k \rightarrow \infty} \mathrm{reg}_{\mathrm{RFP}}[e_{2k+1}^x](1)$ do? Gottfried Ultimate Fellow Posts: 770 Threads: 120 Joined: Aug 2007 11/02/2010, 12:20 PM (11/01/2010, 08:32 PM)mike3 Wrote: offset so it equals 1 at 0). Now, what does $\lim_{k \rightarrow \infty} \mathrm{reg}_{\mathrm{RFP}}[e_{2k+1}^x](1)$ do?Hi Mike - Hmm I tried with n=5,n=17,n=27 and got the according Bell-matrices. Using integer heights iteration worked as expected. I tried fractional heights, h=0.5,h=0.25 at x=0 and x=1 and the series with truncation at 64 coefficients do not converge well, not even having alternating signs. So I couldn't discern any interesting result so far... Would you mind to give some more hint? Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post My interpolation method [2020] tommy1729 1 1,508 02/20/2020, 08:40 PM Last Post: tommy1729 Kneser method question tommy1729 9 5,966 02/11/2020, 01:26 AM Last Post: sheldonison Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 1,313 09/09/2019, 10:55 PM Last Post: tommy1729 2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,557 12/21/2016, 01:27 PM Last Post: tommy1729 Tommy's matrix method for superlogarithm. tommy1729 0 2,541 05/07/2016, 12:28 PM Last Post: tommy1729 [split] Understanding Kneser Riemann method andydude 7 11,976 01/13/2016, 10:58 PM Last Post: sheldonison Kouznetsov-Tommy-Cauchy method tommy1729 0 2,864 02/18/2015, 07:05 PM Last Post: tommy1729 Problem with cauchy method ? tommy1729 0 2,723 02/16/2015, 01:51 AM Last Post: tommy1729 picturing method. tommy1729 4 6,043 07/03/2014, 08:23 AM Last Post: tommy1729 fake id(x) for better 2sinh method. tommy1729 5 7,445 06/05/2014, 08:21 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)