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 Iterability of exp(x)-1 jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 08/13/2007, 09:06 PM (This post was last modified: 08/13/2007, 09:08 PM by jaydfox.) The logarithm is "entire" for reals > 0 (not quite "entire", but you know what I mean), but it's standard power series diverges outside the range (0, 2]. Analytic extension is used outside that range. So this function might only converge for x<=1. Besides, you do know what the formula equals at x=5, don't you? Well, for starters, at x=4, it's approximately 5.03481484682034616908489989276E+41. Bear in mind, this function is equal to the second iterated logarithm (base e) of my cheta function, shifted by a constant in the x direction. So it has tetrational growth. It's like trying to solve sin(x) using the power series, and then saying it appear divergent because you tried to solve the power series for x=100. So no worries. Just make sure it converges for x=3, which should equal 96.0223655650268799109865292599. ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread Iterability of exp(x)-1 - by bo198214 - 08/11/2007, 09:33 PM RE: Iterability of exp(x)-1 - by Daniel - 08/11/2007, 09:49 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/11/2007, 11:42 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/12/2007, 09:07 AM RE: Iterability of exp(x)-1 - by jaydfox - 08/12/2007, 04:41 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 08:54 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/11/2007, 10:25 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 09:06 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 09:13 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 09:16 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 09:33 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 10:00 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:05 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 10:11 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:22 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:00 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 10:29 PM RE: Iterability of exp(x)-1 - by andydude - 08/13/2007, 10:30 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:39 PM RE: Iterability of exp(x)-1 - by andydude - 08/15/2007, 08:36 AM RE: Iterability of exp(x)-1 - by bo198214 - 08/15/2007, 09:21 AM RE: Iterability of exp(x)-1 - by andydude - 08/15/2007, 08:40 PM RE: Iterability of exp(x)-1 - by jaydfox - 08/15/2007, 08:54 AM RE: Iterability of exp(x)-1 - by jaydfox - 08/15/2007, 08:53 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/15/2007, 09:13 PM RE: Iterability of exp(x)-1 - by bo198214 - 08/20/2007, 04:14 PM RE: Iterability of exp(x)-1 - by andydude - 09/05/2007, 08:15 PM RE: Iterability of exp(x)-1 - by bo198214 - 09/07/2007, 02:45 PM RE: Iterability of exp(x)-1 - by Gottfried - 03/15/2008, 09:13 AM RE: Iterability of exp(x)-1 - by bo198214 - 03/15/2008, 01:14 PM RE: Iterability of exp(x)-1 - by Gottfried - 03/15/2008, 08:25 PM RE: Iterability of exp(x)-1 - by Gottfried - 03/18/2008, 10:14 AM

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