An Epic Gaussian Diamond Fraction - Solving the Recurrence Relation [ Part 2 ]

Today we continue talking about another epic diamond fraction shape :) We solve the recurrence relation / difference equation we've established last time and receive a very nice gamma boi! Other than that, we talk about the limit as n approaches infinity! Enjoy! :3

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[angelmendez-rivera]

9:25 - 9:30 I assume you meant to say Γ(n + 2)^2, since Γ(n) = (n – 1)! for all positive whole numbers n, so applying the unit shift operator twice results in Γ(n + 2) = (n + 1)!.

You can also analytically continue it by using 2^z/Γ(z + 2)^2·[3 – exp(iπz)]/2 instead. It really is a matter of preference. Your continuation is just the real part of the expression I just wrote.

[emanuelvendramini]

Man ... Such a beautiful diamond ... I was almost crying for so much beauty.

[carlosdecabodelavega]

0:16 My son will be forever traumatized.

[gregoirej]

Thank papa flammy !!! It’s always a pleasure to watch your videos ! Could you do a video explaining origins of gamma function, it’s role, etc ?

[RCSmiths]

These fractions are so unique man! Really well done here!

[SAAARC]

That quote at 0:16 is actually so meaningful, thanks papa

[timburdack]

Omg! The beginning, so true! 😂😂😂😂👍👍 You're the best!

[benjaminbrady]

Girlfriend joke hit harder than dad's whip

[hoodedR]

4:31 Aha, jokes on you I have a girlfriend. Also, aren't you married..😂

[muhammedmrtkn]

36th root of "789578687047901181" is very close to "π"

[ishansen]

0:18 Now what is the word "*fap*" here for!!!???? 😂😂🤣🤣🤣🤣🤣🤣

[phoebedraper]

I really like these diamonds! Are there any more planned?

[alirezaghadami]

2:53

Ha ha - French papa,
I'm a French speaker, your French is great 👍"Relation de recurrence"

[VaradMahashabde]

Some *R* → *R* continuations :
2^(x+sin^2(x*π/2))/((n+1)!)^2

2^x * (1+sin^2(x*π/2))/((n+1)!)^2

(2^ceil(x/2)/(n+1)! )^2 (Discontinuous)

[VaradMahashabde]

Papa Flammy : Oh right mathematicians don't have girlfriends, they have wifes

[sahilbaori]

That arithemethicc T-shirt looks dope.

[muradbashirov]

The sound of this chalk, umm delicious

[alexakalennon]

One like for the denglisch ( or maybe genglish)
Like your videos.
Greatings from Germany

[Oler-yxxj]

5:38 Papa Flammy: Jokes about "iks"
Me (Russian): I don't understand! Is it a joke about pronunciation of "six"?

[joefaber]

10:45 Can I also wright it down like this: 2^(floor(n+1/2)×2) ?