Playing two gammas

🌟Support the channel🌟
Patreon: / michaelpennmath
Channel Membership: / @michaelpennmath
Merch: teespring.com/stores/michael-...
My amazon shop: www.amazon.com/shop/michaelpenn
🟢 Discord: / discord
🌟my other channels🌟
mathmajor: / @mathmajor
pennpav podcast: / @thepennpavpodcast7878
🌟My Links🌟
Personal Website: www.michael-penn.net
Instagram: / melp2718
Twitter: / michaelpennmath
Randolph College Math: www.randolphcollege.edu/mathem...
Research Gate profile: www.researchgate.net/profile/...
Google Scholar profile: scholar.google.com/citations?...
🌟How I make Thumbnails🌟
Canva: partner.canva.com/c/3036853/6...
Color Pallet: coolors.co/?ref=61d217df7d705...
🌟Suggest a problem🌟
forms.gle/ea7Pw7HcKePGB4my5

[@theelk801]

can you do a video about how there are other functions which generalize the factorial but the gamma function is the only one that’s logarithmically convex?

[@koendos3]

I don’t mind seeing non-integers being used with the (x)! function, opposed to the gamma function

[@__-cx6lg]

i honestly prefer it that way. it seems like formulas with the gamma function typically have an extra "+1". I don't personally know of any good reason why the gamma function isn't defined to be shifted to line up with the factorial; maybe a historical accident? (or maybe there's a good reason i haven't seen)

[@nadavslotky]

Yes! There is another way to compute it. I can't really write it formally, but with some small alterations, you can turn it into something very similar to the square root of the Wallis product, which itself produces π/2.

[@MrPlaiedes]

He looks like he could go from math to throwing papers pissed in under a second.

[@joeeeee8738]

Defining the factorial with a factorial inside?

[@MortimerADuke]

I would assume, although I don't know for certain, that the factorial used to define the gamma function, the generalized factorial, is the original factorial which only is defined on non-negative integers and just the product of the integers 1 to m. This would mean that it is generalized not with itself, but rather with a non-generalized, and therefore different, form.

[@tarikb.9497]

This one was literally too fast 😄😄😄

[@rshawty]

For the last limit I think by using the Stirling formula, some things cancel each other out and make it easier to calculate

[@multicellll]

Ya will try it on my OWN .. sure sure

[@carultch]

Why is the Gamma function shifted from the original factorial operation?

[@yanns09]

You defined z! With a limit containing a factorial

[@KirkWaiblinger]

It's using it on natural numbers only though

[@PixelSergey]

How do you actually calculate values for the gamma function?

[@MrMarewx]

Quantity of stains on your tshirt goes to infinity 😂

[@euleri0]

missed sterlings approx

[@dcthatsme]

I know some of these words

[@sharpnova2]

maybe wrong channel for you. you could go learn a little more and come back. it's worth it.

[@LadyMFUnicorn]

Math ❤

[@roberttelarket4934]

Are you playing games again Mike?

[@Kenjuudo]

He's playing Factorio.

[@sharpnova2]

resulting in a series formula for pi