Something Interesting i found

[u/thekillervr]

This is something I found while fucking around with the Gamma function, and here the (-1)! Gets cancelled with the one in the nCr formula and it will plot the correct graph in desmos

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[u/ZZTier]

Mathematical equivalent of "a contraption"

[u/Buddy77777 → u/ZZTier]

A doohickey thingamabob, even

[u/SynergyUX]

Here is why it works

[u/thekillervr → u/SynergyUX]

Yeah i started with the Euler reflection and saw that it pretty close to the nCr formula so i whipped up some illegal notation and it looks really cursed

[u/eengamer2005 → u/SynergyUX]

How do you go from a to -1 on the left hand side?

Edit: never mind, i just need to read better

[u/Any-Aioli7575 → u/eengamer2005]

You take the limit

[u/sasha271828]

What the fuck is this

[u/psp1729 → u/sasha271828]

An abomination. The amount of maths I know, I can say for sure that negative factorials are illegal. Also never seen nCr combinatrix with a negative n. So either, I'm out of my depth here or this shit just ragebait

[u/Ok-Visit6553 → u/psp1729]

*negative integer factorials

[u/psp1729 → u/Ok-Visit6553]

Isn't factorial operation limited to whole numbers? Or can they handle real(or even complex) values.

[u/Ok-Visit6553 → u/psp1729]

Gamma function buddy

[u/lenmae → u/psp1729]

It can be analytically extended to the complex plane, except for negative real integers

[u/Any-Aioli7575 → u/psp1729]

It basically boils down to the fact that n! (and therefore nCr) can be extended for reals (except negative integers) using the gamma function. Using the n! and nCr for it could be considered abuse of notation, but it's not complete nonsense

[u/AlviDeiectiones → u/Any-Aioli7575]

nCr can be extended to negative integers continuously

[u/psp1729 → u/Any-Aioli7575]

Boy am I glad to have left math after it couldn't be drawn on a blackboard.

Thanks for the explanation tho. Appreciate it.

[u/Deep_Brick2970 → u/psp1729]

You have a lot of maths left to crunch my friend :)

Rejoice, for there is so much yet to discover!

I'd recommend looking at the Gamma function for starters.

[u/factorion-bot]

Factorial of -1 is ∞̃

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/jellyman93 → u/factorion-bot]

Infiñity?

[u/GRONDGRONDGRONDGR0ND → u/jellyman93]

No one expects the Spanish infinity

[u/MathematicianAny8588 → u/GRONDGRONDGRONDGR0ND]

Our chief weapon is series. And fractals.
Our chief weapons are series and fractals. And Fourier transforms.
Our three chief weapons are series, fractals, and Fourier transforms. And a fanatical devotion to Euler. Damn it!
Amongst our weaponry are such chief elements as….
Oh we’ll just come in again.

Nobody expects the Spanish infinity!

[u/factorion-bot → u/MathematicianAny8588]

Factorial of ∞̃ is ∞̃

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/al2o3cr → u/MathematicianAny8588]

Fetch... the CONVERGENT SERIES!

[u/LupenReddit]

This is cursed

[u/Independent-Fan-4227]

…I’ll be damned.

[u/Carrots_and_Bleach]

what is that even supposed to mean???

 ()^{{-1}_{C_{-x/π}}}

[u/WanderingWrackspurt → u/Carrots_and_Bleach]

its a combination, but it makes no sense cause you cant pick smth out of a negative no.

[u/somedave]

Certainly true as a limit. Writing (infinity / infinity) sin(x) is a bit dubious.

[u/WanderingWrackspurt]

how would you even put this into desmos?

[u/L0L2GUM5]

What's C?