1,650 reputation
1414
bio website go.helms-net.de
location Germany
age 61
visits member for 3 years, 9 months
seen 24 mins ago
Mathematics is only a hobby - although I have done undergrad courses in the 70ties. But part of my job was doing statistics and this kept me near my favourite subject "linear algebra" (programmed factor-analysis and a matrix-orientated calculator MatMate). Around 2002 I came in contact with the internet-community in math-newsgroups and could improve my Collatz-discussion. Next subject was the Bernoulli-numbers, then integer matrices and since 2006 the problem of iterated exponentiation aka tetration. Serving half-term jobs in teaching here at the university I found time to fiddle with that subjects in depth - and found love with the exploratory approach and impulse of the 18'th century numbertheory, namely L.Euler, "the master of us all"... Due to lack of formal education I've to do my "research" widely on my own - but that's what I just like: to find structure, pattern, laws from the ground.

5h
accepted Is that series-transformation known in the context of divergent summation?
5h
answered Is that series-transformation known in the context of divergent summation?
13h
awarded  Revival
18h
revised How this expression leads to the given sequence
improved explanation, added improved picture
18h
revised How this expression leads to the given sequence
edited body
19h
revised How this expression leads to the given sequence
added 1183 characters in body
1d
answered procedure-based (as opposed to definition-based) concepts
Apr
1
comment Can you overcome the 6th degree obstruction?
One could try to make things less insulting simply be the (still extremely impolite and illiterate) <???>son and <???>son (possibly with a plea for excuse not knowing better) to indicate that "Something" is not meant as a jovial/colonialistic game-of-name. (Just a proposal)
Apr
1
comment Is there a known solution to $f(x) = (1-x)f(x^2)$?
:-) Yes, I'm so used to the ps to pdf-conversion by ghostscript in the background that I even forget to mention it...
Apr
1
answered Is there a known solution to $f(x) = (1-x)f(x^2)$?
Mar
16
revised Is that series-transformation known in the context of divergent summation?
added image whowing the range of summability
Mar
1
comment Collatz dropping times aperiodicity
(cont) I forgot to mention: the a-periodicity guarantees, that this does not run into a repeated sequence of only one letter but can be continued forever to sharper compressions. If we write the sequence instead as infinite product, beginning with (3/2)*(3/2)*(3/4)*... where we take care that we never fall below 1, then the compression as words provide the "best approximations" of powers of 3 to powers of 2.
Mar
1
comment Collatz dropping times aperiodicity
even more interesting: there are two types of partial sums, say $a=1,2$ and $b=1,2,2$. Then you can rewrite it $a_1(n)=a,a,a,b,a,a,a,b,a,a,b,a,a,a,b,...$ ,say. THis has again two types of "words",$c=a,a,a,b$ and $d=a,a,b$, say. Then one can rewrite this as $a_2(n) = c,d,d,d,c,d,d,c,d,d,d,....$. Then this has two types of "words"... and so on. It is a nice game to find the ever more compressed expression, and is also related to the continued fraction of log(3)/log(2) (or log(3/2), dan't have it at hand at the moment)
Feb
16
revised Infinite matrix leading eigenvector problem
added 79 characters in body
Feb
16
revised Infinite matrix leading eigenvector problem
added 863 characters in body
Feb
16
revised Infinite matrix leading eigenvector problem
added 57 characters in body
Feb
16
revised Infinite matrix leading eigenvector problem
added 1098 characters in body
Feb
16
answered Infinite matrix leading eigenvector problem
Feb
16
comment Infinite matrix leading eigenvector problem
I don't know whether you've already observed that the characteristic polynomial factors in terms of q-binomials (with $q=e^{-\lambda}$) depending on the size of the matrix? I've seen this for even sizes. (Maybe this gives some hint for the eigenvalues, too.)
Feb
15
revised Euler's divergent series sum n!*(-1)^n: what is known about the resulting constant?
added 13 characters in body