- #1
Galadirith
- 109
- 0
Hi everyone, I have been having a problem with the General Binomial Coefficient for any rational value:
[tex]
\left(
\begin{array}{c}
n\\
r\end{array}
\right)
= \frac{1}{r!}\prod_{i=0}^{r-1} (r-i)
[/tex]
Now this works fine except when r=0. so 0! is defined to be 1 so the coefficient of the product of the series is 1, but then the cap PI would read:
[tex]
\left(
\begin{array}{c}
n\\
0\end{array}
\right)
= \frac{1}{0!}\prod_{i=0}^{-1} (r-i)
[/tex]
how can that possibly be evaluated, is there a mathematical reason or is it more defined to be 1. I know that this somehow mean the empty product which is defined to be 1, but how is this the empty product. Thanks Guys :-)
[tex]
\left(
\begin{array}{c}
n\\
r\end{array}
\right)
= \frac{1}{r!}\prod_{i=0}^{r-1} (r-i)
[/tex]
Now this works fine except when r=0. so 0! is defined to be 1 so the coefficient of the product of the series is 1, but then the cap PI would read:
[tex]
\left(
\begin{array}{c}
n\\
0\end{array}
\right)
= \frac{1}{0!}\prod_{i=0}^{-1} (r-i)
[/tex]
how can that possibly be evaluated, is there a mathematical reason or is it more defined to be 1. I know that this somehow mean the empty product which is defined to be 1, but how is this the empty product. Thanks Guys :-)