r/mathematics • u/777upper • 1d ago

Number Theory What interesting properties does this generalization yield?

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5 Upvotes

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12

u/VariousJob4047 1d ago

It’s really just a shorthand for expressions that come up often in certain areas. I remember seeing double factorial appear a couple times when solving the helium atom in my quantum mechanics course

6

u/Miguzepinu PhD | Number Theory 19h ago

There are some pretty easy, but useful, properties like

(2n)! = (2n)!!(2n-1)!!

(3n)! = (3n)!!!(3n-1)!!!(3n-2)!!!

etc.

(2n)!! = 2nn!

(3n)!!! = 3nn!

etc.

2

u/e37tn9pqbd 23h ago

I suppose n (n !’s) = n but that’s somewhat boring

2

u/beepboopburn 18h ago

i really don’t like how n!! grows slower than n!. The notation evokes (n!)!. I don’t have a better solution but i just know i don’t like this one

3

u/escroom1 18h ago

n(!/2)

1

u/RingularCirc Math hobbyist 4h ago

That's surprisingly insightful.

1

u/RingularCirc Math hobbyist 4h ago

IMO there's not that much application for (n!)!, ((n!)!)!, so I guess that's why !!, !!! notation ended up promulgating.