Gottfried Helms
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 Jul23 revised Does the Borel-transform of the Lerch-Transcendent have a name/simple expression? added 50 characters in body Jul23 revised Does the Borel-transform of the Lerch-Transcendent have a name/simple expression? added 50 characters in body Jul23 asked Does the Borel-transform of the Lerch-Transcendent have a name/simple expression? Jul23 answered Summing Lerch Transcendents Jul22 revised In the definition of Carmichael number, why is it necessary to have $(b, n) = 1$? corrected spell in the title Jul19 comment How to replace addition with multiplication to find the next integer value? @siméon: hadn't just this been the point/the nerve of the couriosity of the OP? Jul18 comment List of divergent series and their summations what about wikipedia? There is already a certain list. Why not extend that list? Jul15 revised Looking for a verification or refutation my attempted proof of why the Collatz conjecture is probably false. added 542 characters in body Jul15 comment Looking for a verification or refutation my attempted proof of why the Collatz conjecture is probably false. Have you ever tried to verify the conjecture that $g(x)=2^x$? I've just rund some tests and tried for instance $g(20)$ so 20 steps to reach 1 (or : how much numbers can be generated if you start by n=1 and do the inverse collatz-transformation for 20 steps?). For that example I got $g(20)=321$ or $g(20)=322$ (depending on whether we count the cycle at 1 as well) This comprises from $71$ unique odd numbers plus $250$ additional even numbers as even multiples of the odd unique numbers (only cofactored by perfect powers of 2). See my answer-box for a listing of the odd numbers Jul15 answered Looking for a verification or refutation my attempted proof of why the Collatz conjecture is probably false. Jul12 comment What is the direction along the edge of a circle called (in English and by chance German)? @Grantwalzer: Well, now I hope it comes out well for your problem and the ideas were helpful in this or that way. Jul11 comment What is the direction along the edge of a circle called (in English and by chance German)? @Grantwalzer: Also "versetzt" is a better term than "verschieben" in this case - because "verschieben" is somehow felt to be a continuous motion while "versetzt" emphasizes the discreteness of the motion. However - why the limitation on "wachsend" (growing). For a general sentence is "verändert" better, because it doesn't imply only one direction of change of radius. Why should the problem for the reader be specialized to that case of "growing"/"expanding"? Jul11 comment What is the direction along the edge of a circle called (in English and by chance German)? Perhaps "Veränderungen des Radius führen zu Verschiebungen der Punkte auf dem Rand (die Verschiebungen sind nicht-stetig)" . This has also a causal notion. To remove this causal notion I'd say "Veränderungen des Radius gehen einher mit Verschiebungen der Punkte auf dem Rand (die Verschiebungen sind nicht-stetig)". The term "Rand" is here a short form for "auf dem Umfang" ("on the circumference"), and possibly is a bit outdated/today too little technical. Jul8 comment A closed form for the series $\sum_{n=1}^{\infty} \frac{H_n^2-(\gamma + \ln n)^2}{n}$ I have a Pari/GP-routine which makes it really simple. It uses sumalt , a procedure for divergent summation (based on Zagier's ideas) on formal powerseries. Possibly in Math'ica this is possible as well. I can post it here if you're interested. (Or search for "stieltjes" and my user name, possible I've already posted that routine here or in MO) Jul8 comment A closed form for the series $\sum_{n=1}^{\infty} \frac{H_n^2-(\gamma + \ln n)^2}{n}$ I assume, the $\gamma$ are the Stieltjes-constants? (I just tried to confirm it numerically using $n=100$,$n=1000$, $n=10000$ and $n=200000$ and seems to approximate Stieltjes $\gamma_1$ and $\gamma_2$ Jul4 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. Jul4 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...) Jul4 answered Algorithm for tetration to work with floating point numbers Jul1 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 Jun23 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...