# Nikolaj K.

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bio website graph.axiomsofchoice.org/… location age member for 2 years, 4 months seen 7 mins ago profile views 1,308

A duck walks into a bar. Animal control is promptly called and the duck is released into a near by park.

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 4h awarded Quorum 1d comment Best way to express 2014 In Austrian german, we have a word for it. This year = heuer. 1d comment Do we need to formally teach the Greek Alphabet? Do you know a reference where I can hear "what sound it makes in greek"? Mar6 comment Are there finitely many interesting theorems? I asked a question two years ago here which is related in spirit. Mar6 accepted How to compute the mean average exponent of the naturals? What is the limit for large numbers? Feb28 revised How to compute the mean average exponent of the naturals? What is the limit for large numbers? edited title Feb27 answered Trouble with $\int_0^\infty e^{-ix^2}\mathrm{d}x$ Feb27 revised How to compute the mean average exponent of the naturals? What is the limit for large numbers? added 107 characters in body Feb27 asked How to compute the mean average exponent of the naturals? What is the limit for large numbers? Feb26 comment Convergence of $\sum_{k=1}^{\infty} \left (\sum_{j=1}^{k}\frac 1 j\right)^{-k}$ @GinKin: Go to WolframAlpha.com and type Sum[Sum[1/j,{j,1,k}]^(-k),{k,1,Infinity}], it converges to $1.68227..$. Can we actually compute that? Thoughts: Every partial sum here is some rational number and the frist three terms in $k$ sum to $\frac{19247}{11979}=1.6067..$. Further, note that $\sum_{j=1}^4\frac{1}{j}=1+1/2+1/3+1/4>2$. So your sum equals $\frac{19247}{11979}+\sum_{k=4}^\infty \frac{1}{\left(2+\varepsilon_k\right)^k}$ with $\varepsilon_k$ some positive numbers. Even for $\varepsilon_k=0$ the remaining sum would only be $\frac{1}{8}$. I tried to compute the consecutive grow. Feb26 answered Show that $\lim_{r \rightarrow 1} \sum_{n=1}^{\infty} r^{2^n}= \infty$ Feb26 comment Convergence of $\sum_{k=1}^{\infty} \left (\sum_{j=1}^{k}\frac 1 j\right)^{-k}$ It would be interesting to see the $(k+1)^{th}$ term expressed in terms of the $k^{th}$ one. Feb26 comment Evaluate $f(x)= {\int_{-\infty}^0\ }\frac{x^2}{e^{x^2}}\operatorname d\!x$ It can be brought to the form $a\int_0^\infty t^{y-1}\mathrm{e}^{-t} \mathrm d t$ which is proportional to the Gamma function. Feb25 revised What is the series expansion of $f(z)\cdot\exp\left({s\,\log(z)}\right)$? deleted 1 characters in body Feb25 revised What is the series expansion of $f(z)\cdot\exp\left({s\,\log(z)}\right)$? added 4 characters in body; edited tags Feb25 comment What is the series expansion of $f(z)\cdot\exp\left({s\,\log(z)}\right)$? @ClaudeLeibovici: Yes, thx. Feb25 revised What is the series expansion of $f(z)\cdot\exp\left({s\,\log(z)}\right)$? added 19 characters in body Feb25 asked What is the series expansion of $f(z)\cdot\exp\left({s\,\log(z)}\right)$? Feb24 revised If $(\cos \alpha + i \sin \alpha )^n = 1$ then $(\cos \alpha - i \sin \alpha )^n = 1$ added 12 characters in body Feb24 answered If $(\cos \alpha + i \sin \alpha )^n = 1$ then $(\cos \alpha - i \sin \alpha )^n = 1$