what is half factorial? (1/2)!=? via. Gamma function

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What Is Half Factorial = ?

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"Guys?! How many ways can I arrange half of this apple?!"
"Oh that's easy √π/2 ways"
"Wut"
"Wut"

DarkMagek

IMO, a nicer/prettier/cooler result is
(-½)! = ∏(-½) = Γ(½) = √π

Regardless, thanks for another fun math excursion!

ffggddss

So, that's technically a FRACTORIAL, right? lol

mangalvnam

Been a long time since I was taught most of this stuff, but never by a teacher who could pull together so many facts to make the job so much easier. Students are lucky today...can watch it over and over, and practice with the tutor right in front of you all day.

machobunny

Someone has been eating too many factOREOS.

ramez

You're like the Bob Ross of math.

guitarraccoon

I study in morocco And my teacher told us to search about it . This video is awesome . I watched before 3 ones but I didn't understood . Now It's more clear for me Thank You

Mohamed-Taha-Lakhnig

Wow, this was very informative and interesting. I love the depth and variety of the topics covered on this channel. Good work man. You are doing a very good job.

MG-hish

I would love if you showed how to find the local minimum of the pi function (between 0 and 1)

MartinPuskin

Very interesting, I love videos that broaden somewhat narrow definitions. I’ll keep this one in my back pocket!

radiotv

Beautiful! Congrants and thanks for all your teaching efforts. Greetings from Colombia 🇨🇴

AlejandroGomez-yxsg

"Is it t^2?"
*"no u"*

NBx

Much better than most tutorials. Thanks for being clear!

avtaras

I'm new to this channel, and I'm pretty much hooked after seeing 3 videos.

mathonthego

One of your best videos! Also de Pi function and the Gamma function!!!

Jacob-uyox

I just remembered what love feels like

gongasvf

This reminds me of the whole 1+2+3+4+...=-1/12 bit. Why? Because "factorial" has a specific meaning (N! = N*(N-1)*(N-2)*...*1) that doesn't apply for non-integers. So the question of "(1/2)! is equal to what?" is a meaningless question, just as "What is the sum of all positive integers?" is a meaningless question.

In both cases, something subtle is going on: the question being asked has slightly changed!

In the (1/2)! case, the question has become "How would factorials work for fractions, while remaining self-consistent?". In the sum of all positive integers, the question has become, "My math has me adding all positive integers, but I know my final answer is finite? How can we self-consistently evaluate this to get a finite result?"

Without the subtle change in the question being asked, the results don't make sense. (1/2)! isn't the combinatorial result of anything. And -1/12 isn't the SUM of all positive integers. In both cases, the math is being extended to handle "what if?" scenarios that in turn help us solve problems quite different from the contexts of the original questions.

uumlau

Sad that you didn't do the gaussian integral from first principles. It's a really nice proof which doesn't take very long and makes it clear where the square root comes from.

beatriceleeknowles

Can the Pi function take negative values for x?

spiritgoldmember

I really like your videos U made my calculus easier LOVE FROM PAKISTAN 🇵🇰

muhammadmubbushirhussain

what is half factorial? (1/2)!=? via. Gamma function

what is half factorial? (1/2)!=? via. Gamma function

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