11,817 reputation
11351
bio website go.helms-net.de
location Kassel, Germany
age 61
visits member for 3 years, 7 months
seen 45 mins 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.


20h
comment Problem with understanding first (and second) derivative of a two-sided infinite series
@Zook: yes, I'm aware of that; but I think this does not apply here because we do not reorder. It's more that I think I have some "fiddling-error" while I'm trying to discuss the formal derivative of a function and then the derivative at some x. I think it must have something to do with this - but I'm not sure...
Apr
20
comment Why do we assign values to divergent series?
The question is not about "how" do we assign... but "why" do we assign ("Why do we assign values to divergent series?"). I'm really surprised to see so many answers and comments here which focus the "how"... Well, to give one answer for the "why": it is for completion of the field of possible mathematical operations. One could similarly ask: "why do we assign a value to the squareroot of a negative number?" and answer: just to complete the operation of multiplication - for multiplication of a number with itself and for that operation's inverse.
Apr
17
comment What is the integral $\int x^t/\Gamma(1+t) \, dt$? (In general: relation between series and integrals)
Hmm, I seem to have half the tour. I arrive at the coefficients $a_k$ simply letting Pari/GP give the power series expansion of $\exp(u*t)/\Gamma(1+t)$ in powers of $t$ and let it then determine the formal integral, which of course has a term-by-term approach . I interpret $u$ as $log(x)$ and the first three coefficients of the two variate power-series (in u and t) are your $a_k \cdot k!$. Well, to make the relation completely clear I've to proceed a bit more and go through this on my scribblepad. I'll come back to this then.
Apr
17
comment What is the integral $\int x^t/\Gamma(1+t) \, dt$? (In general: relation between series and integrals)
@chubakueno: hmm, guesswork. After rereading the tag-wiki: likely not a good tag, indeed. Intuitively I think the process in question (systematic relation between series and integrals) is essentially "number-theory" and because I'm an amateur I often think, I'm doing (near) trivia or "elementary" things, so ... (feel free to retag appropriately)
Apr
17
comment What is the integral $\int x^t/\Gamma(1+t) \, dt$? (In general: relation between series and integrals)
@Mathlover: very nice - thank you. That gives a lot to chew for me...
Apr
16
comment What is the integral $\int x^t/\Gamma(1+t) \, dt$? (In general: relation between series and integrals)
A bizarre expression, indeed! I'll try it numerically tomorrow (It's late today)
Apr
16
comment What is the integral $\int x^t/\Gamma(1+t) \, dt$? (In general: relation between series and integrals)
@RonGordon: ah, thanks; I missed it because W/A gave it for the indefinite case without a sign. I've just edited the text.
Apr
16
comment radius of convergence of half iterate of sinh(z)?
@Sheldon: perhaps you might insert this comments as "remark 3" and then we can delete all comments?
Apr
7
comment Good book on analytic continuation?
I found the book of K. Knopp much more readable than G.H.Hardy's and has exercises. However it is a bit old and the newest entry is Euler- and Borel-summation. The specific term "analytic continuation" (and examples) I've found in more contemporary sources much better explained.
Mar
30
comment Find the regularized sum $\frac{1}{\ln(2)}+\frac{1}{\ln(3)}+\frac{1}{\ln(4)}+…$
Hmm, the term $\zeta(x)- {1 \over x-1}$ occured so often lately in my exercises that I think an "incomplete zeta" function should become some standard function in the handbooks (and software). For such an "incomplete zeta" there is also a power series nicely converging at small absolute values of the argument...
Mar
24
comment We know $ \lim_{b \to 1}f_b(n)=n$ when $f_b(n)={b^n -1\over b-1}$ . How can derive the limit for the inverse of $f_b(x)$?
Well, I'd mixed Lhospital and L'Eibniz... Knot in the mind... So, thanks for your answer and working this out.
Mar
24
comment We know $ \lim_{b \to 1}f_b(n)=n$ when $f_b(n)={b^n -1\over b-1}$ . How can derive the limit for the inverse of $f_b(x)$?
Urrgh - it seems I had my mind elsewhere in my comments. They were based on a thinking on a completely wrong path, just deleted them all. Sorry for inconvenience. I'll look at it after a break having a coffee... ;-)
Mar
24
comment We know $ \lim_{b \to 1}f_b(n)=n$ when $f_b(n)={b^n -1\over b-1}$ . How can derive the limit for the inverse of $f_b(x)$?
@Hendrik: We get $\log(0)$ in the denominator (I just included that expression in that formula t make it explicite)
Mar
24
comment Does 'uncountable sequence' make sense?
@Asaf - nice. And your answer gives some really new idea to me; well, naturally: if we think about "gneralizations" as "natural" (which I consider it is). Something to chew on today - thank you!
Mar
24
comment Does 'uncountable sequence' make sense?
(+1) I wanted to ask that same question as a comment in the original thread - but being completely uneducated in "set-theory" and "set theoretic terminology"i decided to stay away. Nice to see that this is not only a complete individualistic sense/feeling...
Mar
22
comment Fractional Calculus: Motivation and Foundations.
@nayrb: motivated by your comment that you've written an undergraduate text about this: I've tried to apply the (fractional) half- derivative to $\zeta(s)$ at $s=0$ exercising various methods but couldn't arrive at a conclusive solution. Would you mind to have a look at my earlier question math.stackexchange.com/questions/375710/… (which I've tried to improve at mathoverflow.net/questions/129620 but didn't find more support)
Mar
20
comment Solving for $3^x - 1 = 2^y$
You do not need Catalan - this is so simple (see @Dan's answer) that even the medieval mathematician Oresme has found it (due to wikipedia)
Mar
19
comment Recurrence of T(n) = T(n/3) + T(2n/3)
Hmmm, the most simple solution is $T(n)=n$ - but as you are not searching for this you might have some additional special constraints in your mind?
Mar
19
comment Given a natural number $a$ find its index in a set of structural descriptions
@GerryMyerson: The q-analogue, I've just inserted it into the text.
Mar
16
comment Very interesting graph!
A nice one is also this one wolframalpha.com/input/?i=plot+sin%28|x|^0.5%2B|y|^0.5%29+%3D+cos+%28‌​x+y%29%2C+%28x%2C-40%2C40%29%2C%28y%2C-40%2C40%29