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authormzuenni <michi.zuendorf@gmail.com>2024-09-10 16:10:54 +0200
committermzuenni <michi.zuendorf@gmail.com>2024-09-10 16:10:54 +0200
commitd12405003fcbe53c26f024bbe1999fc59491046a (patch)
tree4818c6c9918b2174ab38db716647144cf02c8829 /content
parentcf3bf7ef7a3c4899b31041b15bcc67f6607f5cf4 (diff)
fix pentagonal number theorem
Diffstat (limited to 'content')
-rw-r--r--content/math/math.tex2
1 files changed, 1 insertions, 1 deletions
diff --git a/content/math/math.tex b/content/math/math.tex
index bad3bad..dd88a5b 100644
--- a/content/math/math.tex
+++ b/content/math/math.tex
@@ -485,7 +485,7 @@ Die Anzahl der Partitionen von $n$ mit Elementen aus ${1,\dots,k}$.
\begin{align*}
p_0(0)=1 \qquad p_k(n)&=0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0\\
p_k(n)&= p_k(n-k) + p_{k-1}(n-1)\\[2pt]
- p(n)=\sum_{k=1}^{n} p_k(n)&=p_n(2n)=\sum\limits_{k\neq0}^\infty(-1)^{k+1}\bigg[p\bigg(n - \frac{k(3k-1)}{2}\bigg) + p\bigg(n - \frac{k(3k+1)}{2}\bigg)\bigg]
+ p(n)=\sum_{k=1}^{n} p_k(n)&=p_n(2n)=\sum\limits_{k=1}^\infty(-1)^{k+1}\bigg[p\bigg(n - \frac{k(3k-1)}{2}\bigg) + p\bigg(n - \frac{k(3k+1)}{2}\bigg)\bigg]
\end{align*}
\begin{itemize}
\item in Formel $3$ kann abgebrochen werden wenn $\frac{k(3k-1)}{2} > n$.