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 Series of tetrates:consecutive bases Gottfried Ultimate Fellow Posts: 757 Threads: 116 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 »

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