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 Interesting value for W, h involving phi,Omega? Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 03/16/2008, 08:14 AM (This post was last modified: 03/19/2008, 07:33 AM by Ivars.) Ivars Wrote:I was studying the graph of selfroot of Lambert function: W(x)^(1/W(x)). It has maximum value at x=(e*(e^e)) and is e^(1/e) ; so W(e*(e^e)) =W(e^(e+1))= e If we use this, we can find : h( (e^(-(e^e)))^e))= h(1,28785E-1 ln((e^(-(e^e))))^e)= e*ln(e^(-e^e)) = -e*e^e so : h( (e^(-(e^e)))^e))= -W(-ln((e^(-(e^e)))^e))/ln((e^(-(e^e)))^e)= -W(e*e^e)/-e*e^e = -e/-e*e^e = 1/e^e= e^(-e) So: h( (e^(-(e^e)))^e))= h(1,28785E-1= e^(-e) = 0,065988036 and second superroot of ((e^(e^e))^e) = ln(((e^(e^e))^e))/W(ln ((e^(e^e))^e)) = e*(e^e)/W(e*(e^e)) = e*(e^e)/e = e^e= 15,15426224 Ssroot( ((e^(e^e))^e)= ssroot(7,76487E+17) = e^e = 15,15426224 For these values, h(1/a) = 1/ssroot(a) I wonder are there any similar relations for W((1/e)*(e^e)) =W(e^(e-1))= W(5.574..) = 1.3894.. Ivars « Next Oldest | Next Newest »

 Messages In This Thread Interesting value for W, h involving phi,Omega? - by Ivars - 01/18/2008, 12:26 PM RE: Interesting value for W, h involving phi? - by Ivars - 01/18/2008, 10:49 PM RE: Interesting value for W, h involving phi? - by andydude - 01/19/2008, 09:16 AM RE: Interesting value for W, h involving phi? - by Ivars - 01/19/2008, 07:40 PM RE: Interesting value for W, h involving phi? - by bo198214 - 01/19/2008, 10:26 AM RE: Interesting value for W, h involving phi? - by Ivars - 01/19/2008, 08:18 PM RE: Interesting value for W, h involving phi? - by Ivars - 02/01/2008, 09:53 AM RE: Interesting value for W, h involving phi? - by Ivars - 02/01/2008, 08:38 PM RE: Interesting value for W, h involving phi? - by Ivars - 02/10/2008, 09:38 AM RE: Interesting value for W, h involving phi? - by Ivars - 02/20/2008, 12:25 AM RE: Interesting value for W, h involving phi, Omega? - by Ivars - 02/21/2008, 11:35 PM RE: Interesting value for W, h involving Omega, phi? - by Ivars - 02/25/2008, 02:01 PM RE: Interesting value for W, h involving phi? - by Ivars - 02/26/2008, 03:57 PM RE: Interesting value for W, h involving phi? - by bo198214 - 02/26/2008, 06:22 PM RE: Interesting value for W, h involving phi? - by Ivars - 02/26/2008, 08:04 PM RE: Interesting value for W, h involving phi? - by Ivars - 02/28/2008, 02:04 PM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/04/2008, 07:50 AM RE: Interesting value for W, h involving phi,Omega? - by bo198214 - 03/04/2008, 09:09 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/04/2008, 09:29 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/06/2008, 09:53 PM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/06/2008, 10:20 PM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/08/2008, 10:48 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/08/2008, 11:20 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/09/2008, 08:48 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/10/2008, 11:07 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/14/2008, 09:55 PM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/16/2008, 08:14 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/17/2008, 07:23 PM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 03/27/2008, 08:02 AM RE: Interesting value for W, h involving phi,Omega? - by Ivars - 04/04/2008, 01:41 PM

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