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How it looks (i.θ)ₐ
#13
(04/23/2015, 04:52 PM)marraco Wrote: Now, if the basesreally turn into ellipses, then it should be easy to find an algebraic expression for tetration to real exponents, or at least an important insight for

The base seems to match an ellipse with center near c=2.65599203615835 (Don't take that precision as accurate. I got it from Excel), relation of axis b=a, and radius , or


I've been trying to follow this thread, and finally I have something to contribute. For the bases it might be easier to use my expansion of this function. See http://arxiv.org/pdf/1503.07555v1.pdf

I came up with a holomorphic expression for for these bases. It's a fast converging expression as well. It is not as messy as a Taylor series expansion of this same function. It's also a single holomorphic expression for all , greatly reducing computational time.
This is for the periodic/pseudoperiodic extension of tetration (regular koenigs iteration) for bases

The expression isn't so easy to write out:



It is a periodic solution, except at eta.
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Messages In This Thread
How it looks (i.θ)ₐ - by marraco - 04/18/2015, 11:20 PM
RE: How it looks (i.θ)ₐ - by sheldonison - 04/19/2015, 02:40 PM
RE: How it looks (i.θ)ₐ - by marraco - 04/19/2015, 08:40 PM
RE: How it looks (i.θ)ₐ - by sheldonison - 04/19/2015, 11:19 PM
RE: How it looks (i.θ)ₐ - by marraco - 04/20/2015, 02:35 AM
RE: How it looks (i.θ)ₐ - by Gottfried - 04/20/2015, 07:53 AM
RE: How it looks (i.θ)ₐ - by marraco - 04/21/2015, 02:34 AM
RE: How it looks (i.θ)ₐ - by marraco - 04/21/2015, 03:20 AM
RE: How it looks (i.θ)ₐ - by sheldonison - 04/21/2015, 08:23 AM
RE: How it looks (i.θ)ₐ - by marraco - 04/23/2015, 04:52 PM
RE: How it looks (i.θ)ₐ - by JmsNxn - 04/23/2015, 11:15 PM
RE: How it looks (i.θ)ₐ - by sheldonison - 04/23/2015, 11:20 PM
RE: How it looks (i.θ)ₐ - by marraco - 04/26/2015, 12:50 AM
RE: How it looks (i.θ)ₐ - by sheldonison - 04/26/2015, 05:08 AM
RE: How it looks (i.θ)ₐ - by marraco - 04/20/2015, 03:46 AM
RE: How it looks (i.θ)ₐ - by marraco - 04/23/2015, 02:21 AM
RE: How it looks (i.θ)ₐ - by marraco - 04/25/2015, 07:52 PM



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