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 Rational sums of inverse powers of fixed points of e Gottfried Ultimate Fellow Posts: 764 Threads: 118 Joined: Aug 2007 11/21/2007, 08:50 AM (This post was last modified: 11/21/2007, 08:58 AM by Gottfried.) jaydfox Wrote:This post doesn't have much if anything to do with tetration, but I discovered it while analyzing logarithms at the fixed points. I had mentioned this previously: http://math.eretrandre.org/tetrationforu...php?tid=59 The fixed points of e are irrational. However, the sums of the inverse n-th powers are rational.Hmm, how did you compute this actually? I tried it with Henryks fixed-point-formula, getting the reciprocals of the first few fixpoints of e Code:.         0.168376379087-0.707754188785*I // branch 0        0.0333484363677-0.122713337947*I // branch 1       0.0131593793714-0.0691856926303*I      0.00718943124116-0.0482569114994*I      0.00458333618210-0.0370546869791*I      0.00319972064661-0.0300725070538*IDoes this agree with your data? Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 07:55 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 08:11 PM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/20/2007, 08:14 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 08:31 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 08:43 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 09:31 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 01:15 AM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 08:14 AM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/21/2007, 08:50 AM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 09:35 AM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/21/2007, 12:52 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 06:20 PM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/22/2007, 06:25 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/22/2007, 08:32 PM

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