Gottfried Helms
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 Mar13 accepted Has someone seen a discussion of the (divergent) summation of $\sum\limits_{k=0}^\infty (-1)^k (k!)^2$? Sep21 accepted Interpolated Fibonacci numbers - real or complex? Sep4 accepted How is the formal inverse of a power series with constant term developed ( for instance $\cosh^{-1}(x)$)? Aug20 accepted Does the inverse of this matrix of size $n \times n$ approach the zero-matrix in the limit as $\small n \to \infty$? Aug10 accepted Limit of differences of truncated series and integrals give Euler-gamma, zeta and logs. Why? Aug5 accepted What is the family of generating functions for the *rows* of this Stirling-number matrix for whose columns they are $\exp(\exp(x)-1)-1$? Jul13 accepted What is the range of convergence of $\sum_{k=0}^\infty (k \cdot x \exp(-x))^k\cdot {1 \over k!} \cdot {1\over k+1}$? Jul4 accepted A better approximation of $({n \over e})^n$ than by $\Gamma(1+n-1/2)$ ? (Focus is “reverse” to the Stirling approximation) Jul4 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? Apr25 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 $f_b(x)$? Jan24 accepted What is the *correct* (matrix) square-root of $A_2=\begin{bmatrix} 0&-1 \\ 1& 2 \end{bmatrix}$? Nov4 accepted $m \in \{2,6,42,1806,…\}$ - a problem of sum-of-$m$'th powers modulo $m$ Oct30 accepted I've seen “hyperbolic rotation” - from this: generalization to multisection rotation: is this possible? Oct9 accepted Problem with the application of the fractional integral (as in wikipedia) , example $f(x)=\exp(x)-1$ Sep25 accepted If I know that a polynomial (of order $k \gt 2$) has at most $1$ positive real root - can I find that easily? Sep18 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)? Sep13 accepted What is the name for defining a new function by taking each k'th term of a power series? Aug13 accepted How to determine the series for $f(x) = \sqrt{1-\sqrt{1+\sqrt{1-\sqrt{1+x}}}}$ around $0$? Jul23 accepted Iterates of $f_b(x) = x - \log_b(x)$ - for $\log(b) \approx 0.399$: convergence to accumulation points or chaos? Jul18 accepted Ratio of sum of Euler's totient to $n$: $\lim_{n \to \infty} {\log \left( \sum_{k=2}^n \varphi(k) \right) \over \log(n)}$