2,224 reputation
1520
bio website go.helms-net.de
location Germany
age 62
visits member for 4 years, 10 months
seen 3 hours ago

Mathematics is only a hobby - although I have done undergrad courses in the 70s. 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-time 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.


May
7
awarded  Nice Answer
Mar
26
comment On an example of an eventually oscillating function
I've found heuristically more properties of $d(x)$, detailed that aspects and gave some hypothetical explanations but still cannot provide proofs. So my followup-question (and possible answeres) might be interesting. Please see here mathoverflow.net/questions/201098
Mar
26
revised Oscillation aspects of two-way infinite alternating series (a followup from the MO-question “functions that eventually oscillate”)
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Mar
26
revised Oscillation aspects of two-way infinite alternating series (a followup from the MO-question “functions that eventually oscillate”)
added 262 characters in body
Mar
26
asked Oscillation aspects of two-way infinite alternating series (a followup from the MO-question “functions that eventually oscillate”)
Mar
16
revised 3n+1 problem and cycles
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Mar
16
revised 3n+1 problem and cycles
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Mar
16
answered 3n+1 problem and cycles
Mar
15
comment 3n+1 problem and cycles
The "cycle" and the "divergence"-problem are likely unrelated. In the $5x+1$-problem we have cycles, and likely most trajectories diverge. In the $3x+1$-problem where we did not yet find any indication of a divergent trajectory, we have nontrivial cycles in the negative numbers.
Mar
15
answered Collatz property implying infinite “fall below” trajectories, is it known?
Mar
10
revised On an example of an eventually oscillating function
rewrote the whole answer, deleted overcomplicated derivations
Mar
4
revised On an example of an eventually oscillating function
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Mar
3
revised On an example of an eventually oscillating function
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Mar
2
revised On an example of an eventually oscillating function
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Mar
2
revised On an example of an eventually oscillating function
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Mar
2
revised On an example of an eventually oscillating function
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Mar
2
revised On an example of an eventually oscillating function
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Mar
2
answered On an example of an eventually oscillating function
Feb
28
comment On an example of an eventually oscillating function
Hmm,I just tried to get some advantage from a reformulation for $x$ near $1$, so using $x=1-t$ and then to centralize (+ smooth) the oscillation of the result around $1/2$ by writing $g(t)=((1-t)-1) - ((1-t)^2-1)+((1-t)^4-1) - ... + ... $ and $f(x)=g(1-x)+1/2 $), then expand the binomial expressions (by the powers of $(1-t)$ and collect like powers of $t$. This gives at each power of $t$ an infinite divergent series but which is alternating and can be normalized by decomposition into geometric series. This gives vanishing coefficients at the $g(t)$-series. But I've not yet arrived anywhere...
Feb
21
revised A question on Collatz's conjecture
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