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open problems survey
#14
In generalization of (the already solved) TPID 6 and following this thread of Andrew:

Does the sequence of interpolating polynomials of the points defined by pointwise converge to a function on (0,oo) (, satisfying )?

If it converges:
a) is then the limit function analytic, particularly at the point ?
b) For let b[4]x be the regular superexponential at the lower fixpoint. Is then f(x)[4]x = x for non-integer x with ?
c) For let b[4]x be the super-exponential via Kneser/perturbed Fatou coordinates. Is then f(x)[4]x = x for non-integer x with ?

To be more precise we can explicitely give the interpolating polynomials:
,
the question of this post is whether
exists for each .
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Messages In This Thread
open problems survey - by bo198214 - 05/17/2008, 10:03 AM
Exponential Factorial, TPID 2 - by andydude - 05/26/2008, 03:24 PM
Existence of bounded b^z TPID 4 - by bo198214 - 10/08/2008, 04:22 PM
A conjecture on bounds. TPID 7 - by andydude - 10/23/2009, 05:27 AM
Logarithm reciprocal TPID 9 - by bo198214 - 07/20/2010, 05:50 AM
RE: open problems survey - by nuninho1980 - 10/31/2010, 09:50 PM
convergence of self-tetra-root polynomial interpolation. TPID 12 - by bo198214 - 05/31/2011, 04:54 PM
Tommy's conjecture TPID 16 - by tommy1729 - 06/07/2014, 10:44 PM
The third super-root TPID 18 - by andydude - 12/25/2015, 06:16 AM

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