# Limit of sum of factorials/beta functions

• October 12th 2008, 01:10 PM
ory
Limit of sum of factorials/beta functions
Hi people.
I am faced with the following limit:
$$lim_{k \rightarrow \infty} \left( \sum_{j=2}^k \frac{{k+a-j-1 \choose {k-j}}}{B(j+b,c)} \right)$$
where a \in N, (b,c) \in R^2 constants, and B(j+b,c) the standard beta function. Of course the choose function can be expressed as a beta as well.
Can anybody help?
• October 12th 2008, 02:18 PM
Plato
Quote:

Originally Posted by ory
Hi people.
I am faced with the following limit:
$
\lim_{k \rightarrow \infty} \left( \sum_{j=2}^k \frac{{k+a-j-1 \choose {k-j}}}{B(j+b,c)} \right)$

where $a \in N, (b,c) \in R^2$ constants, and B(j+b,c) the standard beta function. Of course the choose function can be expressed as a beta as well.
Can anybody help?