Reputation
14,442
Next privilege 15,000 Rep.
Protect questions
Badges
1 21 62
Impact
~298k people reached

21h
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 $f(f(x))=x^2+x$?
added 1379 characters in body
Jun
17
revised How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
added 67 characters in body
Jun
17
revised How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
added 63 characters in body
Jun
17
revised How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
added 9320 characters in body
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”?
added 46 characters in body
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 $?
added 13 characters in body
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 $?
added 199 characters in body
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 $\lim_{n \to \infty} s_n / n = 0$
Jun
6
comment Cesàro means of divergent series
@theodoricus : $\ln(2)$. Even more general: once the cesaro-sum/mean converges at all, then it converges to the value which is expected by the other computation / estimation techniques. And the alternating harmonic series converges itself to the same value $\ln(2)$
Jun
6
comment general term of a given sequence
Besides the comment of @Deepak: if there are multiple ways to express the general term I would also look for one which can also be generalized to fractional $n$. Introducing something like $\cos( n \pi/2 )$ and $\sin( n \pi/2 )$ for this (replacing the bracketed terms), the formula of the handbook seems more promising for me.
Jun
5
answered Proof of $\sum_{x = 1}^\infty \frac{1}{x}$'s divergence by absurdity?