), we’re going to use math.

So, let’s say you have some number s and another number z that represents the size of the thing you want to fit inside something else. The lower gamma function is basically calculating how many times you can fit things with a volume of z into something with a total volume of 1 (which we’ll call “the universe”).

Here’s the formula:

Γ(s,z) = e^(-z) * sum from k=0 to infinity of z^k / [k! * (s+k)]^(s+k)

Now, if you’re like me and your eyes just glazed over at that equation, let’s break it down. The first part is e^(-z), which basically means “the opposite of the number z raised to the power of -1”. So if z is 5, then e^(-z) would be about 0.0067 (rounded to two decimal places).

The second part is a summation that starts at k=0 and goes all the way up to infinity. Inside this summation, we have another expression: z^k / [k! * (s+k)]^(s+k) . This basically means “the number z raised to the power of k divided by the factorial of k multiplied by the factorial of s plus k”.

So if you wanted to find out how many times something with a volume of 5 could fit inside something else with a total volume of 10, you would plug in those numbers for z and s:

Γ(s=3,z=5) = e^(-5) * sum from k=0 to infinity of (5)^k / [k! * (3+k)]^(3+k)

And that’s it! You now have the lower gamma function for finding out how many times something can fit inside another thing. It might not be as exciting as fitting marshmallows in a box, but at least you won’t get any sticky residue on your calculator.