From d12405003fcbe53c26f024bbe1999fc59491046a Mon Sep 17 00:00:00 2001 From: mzuenni Date: Tue, 10 Sep 2024 16:10:54 +0200 Subject: fix pentagonal number theorem --- content/math/math.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'content/math') 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 $\frac{k(3k-1)}{2} > n$. -- cgit v1.2.3