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Dmitrii Kouznetsov's Tetration Extension
#11
Kouznetsov Wrote:
bo198214 Wrote:In formulas (3.2), (3.3), (3.4), (3.6), (4.4) you always omit the minus sign in front of the 1 below the log. Only in the computation formula 4.2 the minus sign is at the right place.
Do you mean paper at http://www.ils.uec.ac.jp/~dima/PAPERS/2008analuxp.pdf ?
There is no log in formula (3.2), is there?
Yes I mean that paper. In (3.2) there is not yet the logarithm but in the following formulas. Its just the 1 in the denominator of the second summand that has to be changed into a -1. There are also some minor corrections for the description of the path on page 6 A.,C.: instead of just writing or you have to add the corresponding 1's, as you mention before . But that didnt injure the readability.

Quote:Now I have doubts about (3.3); I remember I had to play with phases manually combinig the logarithms; both Mathematica and Maple failed to do it as I wanted.
Can you reproduce Figure 2? Could you show it?

Unfortunately I am not the deep into the matter and also not familiar with complex function visualization. Hm, does that mean that I can not just take the normally cutted logarithm but have to use something else?

I dint get you algorithm to work, it does always diverge. Though I use not Laguerre Gauss integration but simple equidistant integration this shouldnt stop the convergence. Can you send me a sample of your code?

Quote:Yes, I assume , but it follows from the analyticity and the assumption that is real at z>-2.
Oh I wasnt aware of this.
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Messages In This Thread
RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/18/2008, 05:09 PM

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