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 Deriving tetration from selfroot? Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 03/25/2008, 05:52 PM (This post was last modified: 03/25/2008, 06:02 PM by Ivars.) Selfroot is x^(1/x): Selfroot = $x^{1/x}= e^{\ln(x^{(1/x})}=e^{(\ln(x)/x)}*e^{+-(2*\pi*I*{k/x)}$ For Imaginary x, ${\ln(x)/x}$ will be imaginary, of the form: ${+-{(({1/2}+n)/x)}*\pi*I$ so roots are: $e^{+-{(({1/2}+n)/x)}*\pi*I }*e^{+-(2*\pi*I*{k/x)}$, again infinite quantity in totality. n=0 gives: $e^{+-{(({1/2}+n)/x)}*\pi*I}*e^{+-(2*\pi*I*{k/x)}$, If $x=I$ $I^{1/I}=e^{+{(({1/2}+n)/I)}*\pi*I }*e^{+-(2*\pi*I*{k/I)}$, $I^{1/I}=e^{+({1/2}+n)*\pi}*e^{+-(2*\pi*k)}$, For n=0, k=0 $I^{1/I}=e^{+({1/2})*\pi} = e^{\pi/2}$, Something wrong again; I will correct later. Ivars « Next Oldest | Next Newest »

 Messages In This Thread Deriving tetration from selfroot? - by Ivars - 03/12/2008, 08:26 AM RE: Deriving tetration from selfroot? - by Ivars - 03/20/2008, 05:36 PM RE: Deriving tetration from selfroot? - by Ivars - 03/20/2008, 09:53 PM RE: Deriving tetration from selfroot? - by Ivars - 03/21/2008, 07:51 AM RE: Deriving tetration from selfroot? - by Ivars - 03/21/2008, 11:31 PM RE: Deriving tetration from selfroot? - by Ivars - 03/22/2008, 09:52 AM RE: Deriving tetration from selfroot? - by bo198214 - 03/22/2008, 11:28 AM RE: Deriving tetration from selfroot? - by Ivars - 03/22/2008, 02:23 PM RE: Deriving tetration from selfroot? - by Ivars - 03/22/2008, 03:08 PM RE: Deriving tetration from selfroot? - by Ivars - 03/24/2008, 10:26 PM RE: Deriving tetration from selfroot? - by Ivars - 03/25/2008, 05:52 PM RE: Generalized recursive operators - by Ivars - 03/13/2008, 08:01 AM

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