12,903 reputation
11657
bio website go.helms-net.de
location Kassel, Germany
age 61
visits member for 4 years, 1 month
seen 9 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.


Sep
21
accepted Interpolated Fibonacci numbers - real or complex?
Sep
4
accepted How is the formal inverse of a power series with constant term developed ( for instance $\cosh^{-1}(x)$)?
Aug
20
accepted Does the inverse of this matrix of size $n \times n$ approach the zero-matrix in the limit as $\small n \to \infty$?
Aug
10
accepted Limit of differences of truncated series and integrals give Euler-gamma, zeta and logs. Why?
Aug
5
accepted 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 $?
Jul
13
accepted What is the range of convergence of $\sum_{k=0}^\infty (k \cdot x \exp(-x))^k\cdot {1 \over k!} \cdot {1\over k+1}$?
Jul
4
accepted A better approximation of $({n \over e})^n$ than by $ \Gamma(1+n-1/2)$ ? (Focus is “reverse” to the Stirling approximation)
Jul
4
accepted LambertW: $ x=W(x\cdot e^{x}) $ for $ x \ge -1$ but not for $x \lt-1$. How do I express my formula/my text?
Apr
25
accepted We know $ \lim_{b \to 1}f_b(n)=n$ when $f_b(n)={b^n -1\over b-1}$ . How can we derive the limit for the inverse of $f_b(x)$?
Jan
24
accepted What is the *correct* (matrix) square-root of $A_2=\begin{bmatrix} 0&-1 \\ 1& 2 \end{bmatrix} $?
Nov
4
accepted $m \in \{2,6,42,1806,…\} $ - a problem of sum-of-$m$'th powers modulo $m$
Oct
30
accepted I've seen “hyperbolic rotation” - from this: generalization to multisection rotation: is this possible?
Oct
9
accepted Problem with the application of the fractional integral (as in wikipedia) , example $f(x)=\exp(x)-1$
Sep
25
accepted If I know that a polynomial (of order $k \gt 2$) has at most $1$ positive real root - can I find that easily?
Sep
18
accepted Is there a better/closed form for the Cauchyproduct $A^k + A^{k-1}(A+I)/2 + A^{k-2}((A+I)/2)^2 + … +( (A+I)/2)^k$ ($A,I=A^0$ matrices)?
Sep
13
accepted What is the name for defining a new function by taking each k'th term of a power series?
Aug
13
accepted How to determine the series for $ f(x) = \sqrt{1-\sqrt{1+\sqrt{1-\sqrt{1+x}}}} $ around $0$?
Jul
23
accepted Iterates of $f_b(x) = x - \log_b(x) $ - for $\log(b) \approx 0.399$: convergence to accumulation points or chaos?
Jul
18
accepted Ratio of sum of Euler's totient to n: $\lim_{n \to \infty} {\log \left( \sum_{k=2}^n \varphi(k) \right) \over \log(n)}$
Jul
17
accepted Problem with infinite product using iterating of a function: $ \exp(x) = x \cdot f^{\circ 1}(x)\cdot f^{\circ 2}(x) \cdot \ldots $