• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Series of tetrates:consecutive bases Gottfried Ultimate Fellow Posts: 767 Threads: 119 Joined: Aug 2007 10/20/2009, 06:50 PM (This post was last modified: 10/20/2009, 08:19 PM by Gottfried.) Just came across an article, which refers to the alternating series $\hspace{48} s= - \sum_{b=2}^{\infty} (-1)^b *log( (\frac1b)\^\^ ^{\tiny 2})$ whose terms contain the towers of height 2 of reciprocals of consecutive bases. The terms of the series in their original notation are $\hspace{48} (-1)^b * \frac{\log(b)}{b}$ which I converted to $\hspace{48} = \log(b^{\frac1b}) = - log(\frac1b ^{\frac1b})= - log(\frac1b\^\^ ^{\tiny 2})$ The result is -without explicite derivation, but the method was indicated- given as $\hspace{48} s= \log(2)(\gamma - \frac12\log(2))$ Article: Convergence acceleration of series Pascal Sebah and Xavier Gourdon http://numbers.computation.free.fr/Const...eration.ps January 10, 2002 Note: a couple of msgs of mine related to such series you'll find by keyword "tetra-eta-series", which I used earlier Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Perhaps a new series for log^0.5(x) Gottfried 3 1,101 03/21/2020, 08:28 AM Last Post: Daniel Taylor series of i[x] Xorter 12 14,293 02/20/2018, 09:55 PM Last Post: Xorter An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 14,581 01/14/2017, 09:09 PM Last Post: Vladimir Reshetnikov Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 1,947 12/26/2016, 03:01 AM Last Post: tommy1729 2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,000 12/21/2016, 01:27 PM Last Post: tommy1729 Taylor series of cheta Xorter 13 15,466 08/28/2016, 08:52 PM Last Post: sheldonison Why bases 0 2 tommy1729 0 2,103 04/18/2015, 12:24 PM Last Post: tommy1729 on constructing hyper operations for bases > eta JmsNxn 1 3,205 04/08/2015, 09:18 PM Last Post: marraco [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 44,650 03/27/2015, 11:28 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)