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Regular "pentation"?
#13
(03/29/2011, 09:50 AM)Gottfried Wrote: [update:] after I've written the following I got aware, that this should be better threaded under something like "polynomial tetration/pentation" since the basic powerseries for the tetration as I used it here was derived from the "polynomial tetration" using the diagonalization of the truncated real (square) Bellmatrix and its diagonalization - *not* of the triangular Bellmatrix of the regular tetration

While usually I handle the tetration having a series which has the height-parameter in the exponents of its single terms, I played a bit around with a powerseries-representation, and especially a powerseries-epansion for b^^h for b=4 and beginning at x=0 (instead of x=1 as usual). So that powerseries gives b^^0 = 0, b^^1=1,b^^2=4 and so on. Obviously that powerseries has no constant term. It begins like
PHP Code:
b^^h0.938409102074*0.167927302891*h^0.287554406742*h^0.151567019585*h^+... 
and for instance for b^^0.5 = 0.457214343478 .

That isn't going to give the standard version of pentation, then. You're iterating b^^(x-1) instead of b^^x.
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Messages In This Thread
Regular "pentation"? - by mike3 - 05/01/2010, 11:56 AM
RE: Regular "pentation"? - by tommy1729 - 05/01/2010, 03:21 PM
RE: Regular "pentation"? - by bo198214 - 05/01/2010, 08:54 PM
RE: Regular "pentation"? - by mike3 - 05/02/2010, 12:07 AM
RE: Regular "pentation"? - by andydude - 05/02/2010, 09:12 AM
RE: Regular "pentation"? - by Base-Acid Tetration - 05/02/2010, 11:29 PM
RE: Regular "pentation"? - by andydude - 05/03/2010, 02:54 AM
RE: Regular "pentation"? - by mike3 - 05/03/2010, 03:27 AM
RE: Regular "pentation"? - by andydude - 05/07/2010, 03:10 AM
RE: Regular "pentation"? - by andydude - 05/07/2010, 03:17 AM
RE: Regular "pentation"? - by mike3 - 05/07/2010, 06:07 AM
RE: pentation? (Based on "polynomial" tetration) - by BenStandeven - 04/04/2011, 03:16 AM

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