From 45d95c45013bf4ff73570c94c58b7f0212ccdf26 Mon Sep 17 00:00:00 2001
From: mzuenni <michi.zuendorf@gmail.com>
Date: Sun, 8 Sep 2024 22:16:36 +0200
Subject: moved stuff

---
 content/math/tables/numbers.tex | 59 -----------------------------------------
 1 file changed, 59 deletions(-)
 delete mode 100644 content/math/tables/numbers.tex

(limited to 'content/math/tables/numbers.tex')

diff --git a/content/math/tables/numbers.tex b/content/math/tables/numbers.tex
deleted file mode 100644
index 1dc9f38..0000000
--- a/content/math/tables/numbers.tex
+++ /dev/null
@@ -1,59 +0,0 @@
-\begin{expandtable}
-\begin{tabularx}{\linewidth}{|l|X|}
-	\hline
-	\multicolumn{2}{|c|}{Berühmte Zahlen} \\
-	\hline
-	\textsc{Fibonacci}	&
-	$f(0) = 0 \quad
-	f(1) = 1 \quad
-	f(n+2) = f(n+1) + f(n)$ \\
-	\grayhline
-	
-	\textsc{Catalan}	&
-	$C_0 = 1 \qquad
-	C_n = \sum\limits_{k = 0}^{n - 1} C_kC_{n - 1 - k} =
-	\frac{1}{n + 1}\binom{2n}{n} = \frac{2(2n - 1)}{n+1} \cdot C_{n-1}$ \\
-	\grayhline
-	
-	\textsc{Euler} I &
-	$\eulerI{n}{0} = \eulerI{n}{n-1} = 1 \qquad
-	\eulerI{n}{k} = (k+1) \eulerI{n-1}{k} + (n-k) \eulerI{n-1}{k-1} $ \\
-	\grayhline
-	
-	\textsc{Euler} II &
-	$\eulerII{n}{0} = 1 \quad
-	\eulerII{n}{n} = 0 \quad$\\
-	& $\eulerII{n}{k} = (k+1) \eulerII{n-1}{k} + (2n-k-1) \eulerII{n-1}{k-1}$ \\
-	\grayhline
-	
-	\textsc{Stirling} I &
-	$\stirlingI{0}{0} = 1 \qquad
-	\stirlingI{n}{0} = \stirlingI{0}{n} = 0 \qquad
-	\stirlingI{n}{k} = \stirlingI{n-1}{k-1} + (n-1) \stirlingI{n-1}{k}$ \\
-	\grayhline
-	
-	\textsc{Stirling} II &
-	$\stirlingII{n}{1} = \stirlingII{n}{n} = 1 \qquad
-	\stirlingII{n}{k} = k \stirlingII{n-1}{k} + \stirlingII{n-1}{k-1} =
-	\frac{1}{k!} \sum\limits_{j=0}^{k} (-1)^{k-j}\binom{k}{j}j^n$\\
-	\grayhline
-	
-	\textsc{Bell} &
-	$B_1 = 1 \qquad
-	B_n = \sum\limits_{k = 0}^{n - 1} B_k\binom{n-1}{k}
-	= \sum\limits_{k = 0}^{n}\stirlingII{n}{k}$\\
-	\grayhline
-	
-	\textsc{Partitions} &
-	$p(0,0) = 1 \quad
-	p(n,k) = 0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0$ \\
-	& $p(n,k) = p(n-k,k) + p(n-1,k-1)$\\
-	\grayhline
-	
-	\textsc{Partitions} &
-	$f(0) = 1 \quad f(n) = 0~(n < 0)$ \\
-	& $f(n)=\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k+1)}{2})+\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k-1)}{2})$\\
-	
-	\hline
-\end{tabularx}
-\end{expandtable}
-- 
cgit v1.2.3

