From 8d11c6c8213f46f0fa19826917c255edd5d43cb1 Mon Sep 17 00:00:00 2001 From: mzuenni Date: Sun, 28 Jul 2024 22:54:40 +0200 Subject: Test (#4) * update * moved content in subdir * rename file * add test setup * add test setup * add github action * automaticly test all cpp files * timeout after 10s * setulimit and dont zero memory * test build pdf * install latexmk * update * update * ngerman * fonts * removed old code * add first test * added tests * test in sorted order * more tests * simplified test * more tests * fix suffix tree * fixes and improvements * done ust lst directly * fix swap * add links to pdf * fix constants * add primorial * add comment * various improvements * more tests * added missing stuf * more tests * fix tests * more tests * more tests * more tests * fix recursion? * test trie * more tests * only use python temporarily for listings * only use python temporarily for listings * more tests * fix longestCommonSubstring * more tests * more tests * made code more similiar * fix? * more tests * more tests * more tests * add ahoCorasick test + limit 4GB stack size * more tests * fix test * add additional test * more tests * more tests * fix? * better fix * fix virtual tree * more tests * more tests * recursive closest pair * more tests * decrease limit * new tests * more tests * fix name * more tests * add test * new test * more tests * more tests * more tests * more tests * new test and content * new code * new code * larger tests * fix and test * new test * new test * update pdf * remove comments * new test * more tests * more testcases * more tests * increased limit * more tests * more tests * more tests * new tests * more tests * shortened code * new test * add basic tests for bigint * more tests * removed old files * new test * ignore some files * more auto more ccw * fix test * more tests * fix * new tests * more tests * more tests * stronger test * actually verify delaunay... * more tests * fix header * more tests * run tests parallel? * test parralel? * add --missing * separate workflows * test * is the pdf checked? * separate workflows * fix workflow * more workflows --------- Co-authored-by: Yidi --- content/math/tables/binom.tex | 28 ++++++++++++++++++++++++++++ 1 file changed, 28 insertions(+) create mode 100644 content/math/tables/binom.tex (limited to 'content/math/tables/binom.tex') diff --git a/content/math/tables/binom.tex b/content/math/tables/binom.tex new file mode 100644 index 0000000..878a6b0 --- /dev/null +++ b/content/math/tables/binom.tex @@ -0,0 +1,28 @@ +\begin{tabularx}{\linewidth}{|XXXX|} + \hline + \multicolumn{4}{|c|}{Binomialkoeffizienten} \\ + \hline + \multicolumn{4}{|c|}{ + $\frac{n!}{k!(n - k)!} \hfill=\hfill + \binom{n}{k} \hfill=\hfill + \binom{n}{n - k} \hfill=\hfill + \frac{n}{k}\binom{n - 1}{k - 1} \hfill=\hfill + \frac{n-k+1}{k}\binom{n}{k - 1} \hfill=\hfill + \binom{n - 1}{k} + \binom{n - 1}{k - 1} \hfill=\hfill + (-1)^k \binom{k - n - 1}{k} \hfill\approx\hfill + 2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$ + } \\ + \grayhline + + $\sum\limits_{k = 0}^n \binom{n}{k} = 2^n$ & + $\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}$ & + $\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}$ & + $\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\ + + $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}$ & + $\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}$ & + \multicolumn{2}{l|}{ + $\sum\limits_{i = 1}^n \binom{n}{i} F_i = F_{2n} \quad F_n = n\text{-th Fib.}$ + }\\ + \hline +\end{tabularx} -- cgit v1.2.3