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Logarithm reciprocal
#1
Hello all you tetration brainies out there,

looking somewhat deeper into the intuitive Abel function of f(x)=b*x (which is supposed to be log_b(x) however unproven until now), I found a somewhat direct expression of the coefficients, which boils down to the following challenging question:

Let the sequence be defined recursively in the following way for :
and for

Is ?

Does it converge? The following graph of the sequence for , leaves the question open:
   
(The messed up numbers on the left side are due to a bug in sage *sigh*)

An equivalent slightly nicer formulation of the problem

Let the sequence be defined recursively in the following way for :
and for

Is ?

edit: this can be found now as TPID 9 in the open problems thread.
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Messages In This Thread
Logarithm reciprocal - by bo198214 - 07/20/2010, 04:13 AM
RE: Logarithm reciprocal - by tommy1729 - 07/20/2010, 09:11 PM
RE: Logarithm reciprocal - by bo198214 - 07/21/2010, 02:54 AM
RE: Logarithm reciprocal - by bo198214 - 07/24/2010, 02:19 AM
RE: Logarithm reciprocal - by tommy1729 - 07/24/2010, 09:33 PM
RE: Logarithm reciprocal - by bo198214 - 07/24/2010, 11:10 PM
RE: Logarithm reciprocal - by bo198214 - 08/11/2010, 02:35 AM
RE: Logarithm reciprocal - by bo198214 - 07/25/2010, 03:39 PM
RE: Logarithm reciprocal - by Gottfried - 07/26/2010, 12:14 PM
RE: Logarithm reciprocal - by bo198214 - 07/26/2010, 03:56 PM
RE: Logarithm reciprocal - by Gottfried - 07/26/2010, 05:08 PM

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