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Jul
4
comment Algorithm for tetration to work with floating point numbers
Perhaps this (go.helms-net.de/math/tetdocs/ContinuousfunctionalIteration.pdf) is an interesting essay, although it is extremely amateurish (one of my earlier tries to put numbertheoretic puzzles into shape - I had even difficulties to refer to functions having powerseries in the usual way) - I should rewrite this. But it might give a good impression for a first read.
Jul
4
comment Algorithm for tetration to work with floating point numbers
Hmm, I'm not much active on this this days. Look at my oldest postings, I've called that "matrixmethod" (this is perhaps the most fruitful searchable term). And in the beginning I did not know that this all was already known with the term "Carlemanmatrix". There is also some literature on this, look for Aldrovando (the link to the ArXiv by D. Geisler), Eri Jabotinsky, S.C.Woon (perhaps I can come back to this later with more information - we have it extremely hot today which makes it uncomfortable to sort out links...)
Jul
4
answered Algorithm for tetration to work with floating point numbers
Jul
1
comment Super root function
If something useful should exist, it's rather the (analoguous) pentation-"squareroot". Unfortunately the pentation is not remotely so far developed as the tetration. Maybe you find something in the "tetration-forum" math.eretrandre.org/tetrationforum
Jun
23
comment The limit of the alternating series $x - x^2 + x^4 - x^8 + {x^{16}}-\dotsb$ as $x \to 1$
Didn't you see the formula 3.18 at page 100 of your link? They say the following . Amplitude is about (pg 100 formula 3.18): $ 2/\log(2) \cdot | (\Gamma(\pi \cdot I/ \log(2)))| \approx 0.00274922168400 $ and this is alternating around $0.5$. So there is nothing with $0.333...$ and $0.6666...$ in that article...
Jun
23
comment The limit of the alternating series $x - x^2 + x^4 - x^8 + {x^{16}}-\dotsb$ as $x \to 1$
I gave it a +1 although it seems that the result contradicts other (and my own) results because of the lot of serious work in this answer...
Jun
23
comment The limit of the alternating series $x - x^2 + x^4 - x^8 + {x^{16}}-\dotsb$ as $x \to 1$
Dear Abdou, please see also my graphics in the (same )question at MO from february: mathoverflow.net/questions/198665/…
Jun
23
comment The limit of the alternating series $x - x^2 + x^4 - x^8 + {x^{16}}-\dotsb$ as $x \to 1$
You may also look in this identical Mathoverflow question mathoverflow.net/questions/198665 ; some -I think interesting- additional info is in my answer. See mathoverflow.net/questions/198665/…
Jun
17
comment How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
Will, I've just seen, that your $\lambda()$-function down to the Abel-function $\alpha()$ can directly be determined by the use of the log of the Carlemanmatrix F for the function $f(x)$ . I did never know that this is such an easy relation between that two computation-concepts. See the end of my long answer.
Jun
17
revised How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
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Jun
17
revised How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
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Jun
17
revised How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
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Jun
17
revised How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
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Jun
16
comment More numbers between $[0,1]$ or $[1,\infty)$?
As @columbus8myhw mentioned in his comment: which number in the second set is mapped from the 1 in the first set?
Jun
10
revised With infinite size, we can have $P \cdot M = M \cdot D $ (D diagonal) but where $M^{-1}$ does not exist. Can we say “P is diagonalizable”?
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Jun
10
comment Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices?
I've got an answer at MO jun 2015: mathoverflow.net/a/208900/7710 which resolves the problem.
Jun
10
revised What is the family of generating functions for the *rows* of this Stirling-number matrix for whose columns they are $\exp(\exp(x)-1)-1 $?
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Jun
10
revised What is the family of generating functions for the *rows* of this Stirling-number matrix for whose columns they are $\exp(\exp(x)-1)-1 $?
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Jun
7
comment Cesàro means of divergent series
Hmm, also I suspect that at the date of my answer I might not have thought your question correctly to the end because I end with consideration of the sums, not means. I'll look again at this when I've more time
Jun
7
comment Cesàro means of divergent series
Hmm, I'm not sure at the moment, but isn't the mean not just the $n$'th partial (Cesaro) sum divided by $n$? Then a finite Cesaro-sum $s_n$ for $n \to \infty $ should go to $\lim_{n \to \infty} s_n / n = 0$