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Taylor series of upx function
#7
sheldonison Wrote:...
To me, it would seem as if the first couple of derivatives at x=-1,0 were the same for both solutions, than it is likely that they're the same solution, though the two could still diverge in the higher derivatives.

I had submitted the evaluation of the first derivative with 14 (I hope) decimal digits.

In the similar way, the second derivative can be evaluated, and so on.
But I like the approach by Bo: it is better to prove, than to compare the numerical evaluations. We already have proof that no other tetration is allowed to be holomorphic in the complex plane with cutted out set .

By the way, how about to add some small amount of finction
?THis function has all the derivatives along the real axis, and all of them are zero at points 0 and -1.
Consider the modification of tetration to
with corresponding extension from the range [-1,0] usind the recurrent equation. At the real axis, the modified tetration tem has the same "expansion" as the tetration in these points; however, such a modification destroys the holomorphism.
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Messages In This Thread
Taylor series of upx function - by Zagreus - 09/07/2008, 10:56 AM
RE: Taylor series of upx function - by bo198214 - 09/10/2008, 01:56 PM
RE: Taylor series of upx function - by andydude - 10/23/2008, 10:16 PM
RE: Taylor series of upx function - by Kouznetsov - 11/16/2008, 01:40 PM
RE: Taylor series of upx function - by bo198214 - 11/16/2008, 07:17 PM
RE: Taylor series of upx function - by Kouznetsov - 11/17/2008, 04:11 AM
RE: Taylor series of upx function - by bo198214 - 11/18/2008, 11:49 AM
RE: Taylor series of upx function - by Kouznetsov - 12/02/2008, 12:03 PM
RE: Taylor series of upx function - by Kouznetsov - 12/05/2008, 12:30 AM

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