Basic bilateral hypergeometric series
Imagine you have a box of 20 colored marbles. In that box, there are 12 blue and 8 red marbles. Now, imagine you take out 5 marbles randomly from that box.
A basic bilateral hypergeometric series is just a fancy way of figuring out how many ways you can choose those 5 marbles while making sure that a certain number of them are blue and the rest are red.
For example, one possible scenario is that you want to choose 3 blue marbles and 2 red marbles. To figure out how many ways this can happen, you can use the formula for a basic bilateral hypergeometric series.
It looks like this:
$\sum\limits_{n=0}^{min(a,b)} \frac{ \binom{a}{n} \binom{b}{k-n} }{ \binom{a+b}{k}} $
Don't worry, all that formula really means is that you need to add up all the possible combinations of getting 3 blue marbles out of 12 and 2 red marbles out of 8, while making sure you've chosen a total of 5 marbles.
So, to summarize:
A basic bilateral hypergeometric series is a way of figuring out how many ways you can choose a certain number of objects from two different sets, while making sure you have a specific number of objects from each set. It's like playing a game of marbles with a certain number of blue and red marbles and figuring out how many ways you can win by getting a set number of each color.
A basic bilateral hypergeometric series is just a fancy way of figuring out how many ways you can choose those 5 marbles while making sure that a certain number of them are blue and the rest are red.
For example, one possible scenario is that you want to choose 3 blue marbles and 2 red marbles. To figure out how many ways this can happen, you can use the formula for a basic bilateral hypergeometric series.
It looks like this:
$\sum\limits_{n=0}^{min(a,b)} \frac{ \binom{a}{n} \binom{b}{k-n} }{ \binom{a+b}{k}} $
Don't worry, all that formula really means is that you need to add up all the possible combinations of getting 3 blue marbles out of 12 and 2 red marbles out of 8, while making sure you've chosen a total of 5 marbles.
So, to summarize:
A basic bilateral hypergeometric series is a way of figuring out how many ways you can choose a certain number of objects from two different sets, while making sure you have a specific number of objects from each set. It's like playing a game of marbles with a certain number of blue and red marbles and figuring out how many ways you can win by getting a set number of each color.
Related topics others have asked about: