12,741 reputation
11656
bio website go.helms-net.de
location Kassel, Germany
age 61
visits member for 4 years
seen 52 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.


May
20
accepted What is the functional inverse (with respect to $h$ (!)) of $f^{\circ h}(x)={F(h) +x F(h-1) \over F(1+h) +x F(h) }$?
May
15
accepted Half order derivative of $ {1 \over 1-x }$
May
8
accepted $f(x)=\tanh(1+\tanh^{-1}(x))$ or $f:\tanh(x) \to \tanh(x+1)$ is a rational function?
Apr
16
accepted Sum of the Stieltjes constants? (divergent summation)
Apr
6
accepted Has someone seen a discussion of the (divergent) summation of $\sum\limits_{k=0}^\infty (-1)^k (k!)^2 $?
Apr
5
accepted Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
Mar
10
accepted Having $A_1=a+b+c$,$A_2=a^2+b^2+c^2$, $A_3=a^3+b^3+c^3$ - how to get $a,b,c$?
Feb
20
accepted How can I prove my conjecture for the coefficients in $t(x)=\log(1+\exp(x)) $?
Jan
21
accepted How to relate this integral for the $\Gamma$ function to the defining integral of the $\Gamma$
Jan
15
accepted Convergence radius of $\log(\Gamma(\exp(x)))$?
Jan
3
accepted Is my shorter expression for $ s_m(n)= 1^m+2^m+3^m+\cdots+(n-1)^m \pmod n$ true?
Dec
28
accepted What is the derivative of a power series composed with a sum of iterations on x?
Dec
11
accepted When is $1+x+x^2+x^3+… $ and $ {1 \over 1-x} \quad (x \ne 1) $ *not* interchangeable in an algebraic formula?
Oct
2
accepted $(2k+1)^{4k+1} = (2k+1) \pmod {4k+2} $ . . . why?
Aug
3
accepted Polynomial coefficients in exponential-series: how can I convert this into a composite of $\exp(x)$?
Aug
2
accepted Something like : “recursive” harmonic numbers? Where can I read more?
Aug
2
accepted What is the correct terminology to say that $\small f(x)=a+bx+cx^2+…$ can be expressed by $\small g(x)=A(1-x)+B(1-x)(2-x)+C(1-x)(2-x)(3-x)+… $
Jul
2
accepted How can “ $\small {n \over \varphi(n) } \text{ is integer only if } n=2^r \cdot 3^s $ ” simply be shown?
May
5
accepted Is always $\small {rq-1 \over 2^B} \le q-1 $ with natural r,q,B and $\small r,q \in \{1, \ldots, (2^B-1)\} , odd$?
Apr
30
accepted Is always $\small {rq-1 \over 2^B} +1 \le \min(q,r) $ with equality iff $\small q$ or $\small r$ is a divisor…