Bilateral hypergeometric series

Okay kiddo, have you ever played with a deck of cards before? Imagine you have two decks of cards, one deck is red and the other deck is blue. Each deck has 52 cards, and each card has a number on it.

Now, imagine you want to pick a certain amount of cards from each deck (let's say 3 from the red deck and 2 from the blue deck) and add up the numbers on those cards. In this example, you would have 3 cards from a group of 52 and 2 cards from another group of 52.

That's what a bilateral hypergeometric series is! It's a fancy name for a way to find calculations about groups that have some attributes in common, like picking cards of a certain color or type.

This idea of picking a certain number of things from different groups and adding them together is called a series, because you add up the numbers in a sequence.

The word "hypergeometric" is used because we can use a formula (a bunch of math rules) to figure out how many ways we can pick those cards from the decks based on some rules (such as always picking 3 from one deck and 2 from another).

So, a bilateral hypergeometric series is just a way of using math to add up different groups of things based on specific rules. It's like playing a game with cards, but with numbers and formulas instead!