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base holomorphic tetration
#12
(11/06/2009, 11:29 PM)bo198214 Wrote: , , , .



This gives the following unsimplified coefficients of :


One can see that the coefficients are polynomials in with rational coefficients in .
One needs to investigate whether is analytic in with .

I just wanted to unify the variables: with we can write:
, , or shorter, setting and

, , .

The thing is now that Lambert has a singularity at , i.e. if approaches .

The question is whether this singularity gets compensated somehow by the infinite sum.

I want to further simplify the formula: with
,
where are polynomials in with coefficients that are rational functions in .
I hope i dint put errors somewhere;
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Messages In This Thread
base holomorphic tetration - by bo198214 - 11/05/2009, 02:12 PM
RE: base holomorphic tetration - by mike3 - 11/06/2009, 04:15 AM
RE: base holomorphic tetration - by mike3 - 11/06/2009, 11:58 AM
RE: base holomorphic tetration - by bo198214 - 11/06/2009, 12:12 PM
RE: base holomorphic tetration - by mike3 - 11/06/2009, 09:16 PM
RE: base holomorphic tetration - by bo198214 - 11/06/2009, 11:29 PM
RE: base holomorphic tetration - by mike3 - 11/07/2009, 12:23 AM
RE: base holomorphic tetration - by bo198214 - 11/07/2009, 08:17 AM
RE: base holomorphic tetration - by mike3 - 11/07/2009, 08:21 AM
RE: base holomorphic tetration - by bo198214 - 11/07/2009, 09:55 AM
RE: base holomorphic tetration - by bo198214 - 11/07/2009, 04:47 PM
RE: base holomorphic tetration - by bo198214 - 11/08/2009, 05:39 PM
RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:27 PM
RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:25 PM
RE: base holomorphic tetration - by bo198214 - 11/08/2009, 08:44 PM
RE: base holomorphic tetration - by mike3 - 11/08/2009, 09:51 PM

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