Negative half factorial

In this video, I computed negative half factorial using the shifted gamma function.

[GourawRaj-hjjy]

"never stop learning those who stop learning they stop living " ❤❤❤❤❤❤❤❤

[DragomirGąsieniec]

Never stop teaching, cause those who stop teaching stop developing the world

[aguyontheinternet]

3:00 I mean, this isn't actually a problem, because the gamma function also has that neat little quirk of G(z)=z*G(z-1) that factorials have, and it extends it to all _(most**)_ real numbers. So bringing in that formula is perfectly fine

[juanalbertovargasmesen]

Not illegal. It's one of the definitional properties of the Gamma function. If anything, it's at least a theorem.

The only times "it doesn't work" is with negative integers, because there is a pole of multiplicity one at each one of them, but it's otherwise good and dandy.

[ACertainMan]

The entire purpose of extending the fsctorial using the gamma function is to preserve the property that people call "illegal". Like lol.

[Nofaz]

please do for i! (imaginary factorial) :3 very interesting video sir!

[lagomoof]

For Gamma it's a fundamental property that Gamma(z+1) = z·Gamma(z) for (almost) all complex z, so the "illegal" trick is legal here and the answer 2 just falls out. I would not be surprised if those crying foul at "illegal" tricks are also unhappy at something other than a non-negative integer next to the factorial sign. Is using an illegal trick on an illegal factorial twice as illegal, or is it a case of two negatives making a positive?🤔

[stcenturyteachers]

I think, even by just expanding the Then cancel (-1/2)!, remaining with 1/1/2=2. But thanks for the much needed explanations😊😊

[peta]

Would it be so bad for all the parts of mathematics if FACTORIAL method, for instance, would be applied to natural numbers only? What confuses me is the practice of "convenient assumptions" that became bases for further convenient assumptions...and...and then we wonder why we end up with a theory that two "things" can be in multiple places at the same time.

[Apithia]

Does the illegal method work for any value where they exist? Like π and π+1 or -3/2 and -1/2?

[J.B.L]

What about the full cover on differential equations video you promised?

[stefanbergung]

I don't get those Mathematicians.
It doesn't matter, if the Funktion isn't defined for that Range (/set). Only if it remains internally consistent. And if it doesn't, if we can find and define a subset for which it is.
The interpretation comes later.
That is how negative Numbers work. Then complex numbers and less known ones like the NaN's with infinite digits on the left of the decimal point.
It really is just that simple.

[barryzeeberg]

There is a simpler version of the illegal way: (1/2)! = (1/2) (-1/2)! note that the (-1/2)! cancels the same term in the numerator, so we are left with 1/(1/2) = 2. do not need to use sqrt(pi) :)

[FouadBarca-ediv]

Can you make a video telling us how the epsilon bet came about?

[maxforsberg]

You could have done integration by parts by integrating the t^(-1/2) and taking the derivative of e^(-t). You would have ended up with 2* the integral that defines (1/2)! which you calculated in the previous video. Never stop learning.

[jppitol]

Hi, could you do this question? I think you might enjoy it

If g(x) is a polynomial function that satisfies the following relation: g(x) * g(y) = g(x) + g(y) + g(xy) - 2, for all x, y in the real numbers. So, the value of g(3) when g(2)=5 is:
a) 8 b) 10 c) 12 d) 15 e) 18

[YanAfina]

can you solve any number from the Unified State Exam(Russia)?

[TheLhama]

there is a nother way to solve this : (-1/2)!/(1/2)! = (-1/2)!/((1/2)*(-1/2)!) = 1/(1/2) = 2

[yiutungwong]

In the Riemann Paradox and Sphere Geometry System Incorporated...
π = 2

It can solved for 2 = π