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what is f(k) ?

Anonymous Sat 05 Sep 09:06:11 2020 No.12087192 View Reply Original Report

Quoted By: >>12087362 >>12087892

I don't see an obvious form of f(k) -- what am I missing?

Anonymous

Anonymous Sat 05 Sep 2020 09:08:54 No.12087200 Report

Quoted By: >>12087202 >>12087496 >>12088052

For _k_ versus f(k), I have
k . f(k)
0 . 1
1 . 1
2 . 2
3 . 5
4 . 15
5 . 52

Anonymous

Anonymous Sat 05 Sep 2020 09:09:57 No.12087202 Report

Quoted By: >>12087555

>>12087200
oops, I mean the reciprocal of f(k), sorry

Anonymous

Anonymous Sat 05 Sep 2020 10:12:45 No.12087362 Report

Quoted By:

>>12087192
That sum can only converge if k < -1 I believe

Anonymous

Anonymous Sat 05 Sep 2020 10:14:29 No.12087364 Report

Quoted By:

Pythagream theorem =
https://youtu.be/t8LxTauVpJQ

Anonymous

Anonymous Sat 05 Sep 2020 10:16:18 No.12087368 Report

Quoted By:

So you guys like this stuff ...

I may dig up my notebooks

I have a binomial thingy I want to share

It’s good to be among like minded people

Anonymous

Anonymous Sat 05 Sep 2020 10:24:49 No.12087390 Report

Quoted By:

I dunno what planet this is but factorial is only defined for integers . There is the generalized gamma function which is an integral but we never write it as a factorial sign (!) ever.

Anonymous

Anonymous Sat 05 Sep 2020 10:28:34 No.12087394 Report

Quoted By: >>12087401 >>12087423

$<br />f(k) = \frac{k! e}{1+\zeta(-k)}<br />$

Anonymous

Anonymous Sat 05 Sep 2020 10:31:39 No.12087401 Report

Quoted By:

>>12087394

That’s the Reiman zeta function so you need to be careful but it is basically a contour integral around zero if all is kosher

Anonymous

Anonymous Sat 05 Sep 2020 10:35:27 No.12087410 Report

Quoted By:

And if people write x! And they allow non integers then they are assuming you know it is the Gamma function. I guess you could say !x = G(x-1) if you want ... but no one submits papers that way

Anonymous

Anonymous Sat 05 Sep 2020 10:39:52 No.12087423 Report

Quoted By:

>>12087394
this is incorrect, giving f(1) = 12e/11

Anonymous

Anonymous Sat 05 Sep 2020 11:04:55 No.12087496 Report

Quoted By: >>12087555

>>12087200
This is wrong

Anonymous

Anonymous Sat 05 Sep 2020 11:27:27 No.12087555 Report

Quoted By: >>12087961

>>12087496
>>12087202

Anonymous

Anonymous Sat 05 Sep 2020 14:51:21 No.12087892 Report

Quoted By:

>>12087192
Are these the bell numbers?

Anonymous

Anonymous Sat 05 Sep 2020 15:15:23 No.12087961 Report

Quoted By: >>12087969 >>12088052

>>12087555
Still wrong. From that formula $f(0)=\frac{e}{12}$ or it is undefined.

Anonymous

Anonymous Sat 05 Sep 2020 15:18:11 No.12087969 Report

Quoted By: >>12088052

>>12087961
I mean f(0)=-12e

Anonymous

Anonymous Sat 05 Sep 2020 15:45:44 No.12088052 Report

Quoted By:

>>12087961
>>12087969
You mean f(1) here but yeah this >>12087200 is wrong

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