- #1
Meekah
- 2
- 0
I have problem with prooving those two identities. Any help would be much appriciated!
Show that:
a)
[tex]\begin{Bmatrix}
m+n+1\\ m
\end{Bmatrix}
= \sum_{k=0}^{m} k \begin{Bmatrix}
n+k\\k
\end{Bmatrix}
[/tex]
b)[tex]
\sum_{k=0}^{n} \begin{pmatrix}
n\\k
\end{pmatrix}
\begin{Bmatrix}
k\\m
\end{Bmatrix}
= \begin{Bmatrix}
n+1\\m+1
\end{Bmatrix}
[/tex]
Where:
\begin{Bmatrix}
k\\m
\end{Bmatrix}
is a Stirling number of the second kind.
Show that:
a)
[tex]\begin{Bmatrix}
m+n+1\\ m
\end{Bmatrix}
= \sum_{k=0}^{m} k \begin{Bmatrix}
n+k\\k
\end{Bmatrix}
[/tex]
b)[tex]
\sum_{k=0}^{n} \begin{pmatrix}
n\\k
\end{pmatrix}
\begin{Bmatrix}
k\\m
\end{Bmatrix}
= \begin{Bmatrix}
n+1\\m+1
\end{Bmatrix}
[/tex]
Where:
\begin{Bmatrix}
k\\m
\end{Bmatrix}
is a Stirling number of the second kind.