TITLE: What does the $\prod$ symbol mean?
QUESTION [17 upvotes]: This is one of those cases where I would google if I could, but I don't know what to search for.
I've come across this symbol a few times, but I have no clue what it means or what it is called.
$$\prod$$
Furthermore, what are the $\coprod$ and $\amalg$ symbols for?
I could not list all the places I found it, but the one that sparked it was a discussion on solving the Diophantine equation, $\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$.

REPLY [2 votes]: The uppercase Pi $\prod$ symbol stands for the $product$ operator throughout mathematics, just as the uppercase Sigma $\sum$ symbol would describe the sum operator. Think of the following analogy alliteration:
Pi is to a Product ... as Sigma is to a Sum.