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 regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 sheldonison Long Time Fellow Posts: 664 Threads: 23 Joined: Oct 2008 06/23/2013, 11:13 AM (This post was last modified: 06/23/2013, 11:19 AM by sheldonison.) (06/22/2013, 09:55 PM)Gottfried Wrote: .... $\hspace{48} s_0= S (x - t_0)$ where $S(\cdot)$ denotes the Schröder function.Hey Gottfried! So then, the Schröder function of -infinity for base sqrt(2) from the fixed point of 2 turns out to be $s_0 = \lim_{x\to -\infty} S (x - 2) \approx -1.31563054604637354754$. The significance of this value is that it is also the radius of convergence of the Taylor series for the inverse Schröder function, since -infinity is the nearest singularity, so the radius of convergence would be approximately 1.3156. Then we use the inverse Schröder function of $-s_0$ to get Gottfried's number. $z = S^{-1} (-s_0) + 2 \approx 2.7643210400001$ - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/22/2013, 12:52 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by tommy1729 - 06/22/2013, 08:43 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/22/2013, 09:55 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by sheldonison - 06/23/2013, 11:13 AM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/23/2013, 10:20 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by sheldonison - 06/24/2013, 04:09 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/25/2013, 10:45 AM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by sheldonison - 06/25/2013, 01:37 PM

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