/sci/ - Science & Math » Thread #11256505

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Anonymous Fri 27 Dec 04:52:10 2019 No.11256505 View Reply Original Report

Quoted By: >>11256562 >>11256768 >>11257344 >>11257582 >>11257655 >>11257765 >>11258268

you should be able to solve this

Anonymous

Anonymous Fri 27 Dec 2019 04:59:51 No.11256511 Report

Quoted By:

Anonymous

Anonymous Fri 27 Dec 2019 05:02:04 No.11256515 Report

Quoted By: >>11256546

i only know calc 1

Anonymous

Anonymous Fri 27 Dec 2019 05:19:59 No.11256546 Report

Quoted By:

>>11256515
I'm only in College Algebra

Anonymous

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Anonymous Fri 27 Dec 2019 05:29:52 No.11256562 Report

Quoted By: >>11256585 >>11256613 >>11256796 >>11258201 >>11258822

>>11256505

Anonymous

Anonymous Fri 27 Dec 2019 05:47:13 No.11256585 Report

Quoted By:

>>11256562
kek

Anonymous

Anonymous Fri 27 Dec 2019 05:59:58 No.11256613 Report

Quoted By:

>>11256562
Excuse me, I'm a blind retard. You can solve this in one step

Anonymous

Anonymous Fri 27 Dec 2019 07:52:25 No.11256752 Report

Quoted By:

Just use laplace transform at s=1
L(x^37) = 37!
Then multiply by 1/(2*35!) to get 37*18=740-74=666

It should instead say "you should be able to do this in your head"

Anonymous

Anonymous Fri 27 Dec 2019 08:04:27 No.11256768 Report

Quoted By: >>11256809

>>11256505
I dunno like 18 maybe. Im not some science man so I dont even know anything about numbers lol.

Anonymous

Anonymous Fri 27 Dec 2019 08:41:06 No.11256796 Report

Quoted By: >>11256804

>>11256562
Gamma(36) /= 36!
so in the end you get 18*37*36

Anonymous

Anonymous Fri 27 Dec 2019 08:45:30 No.11256804 Report

Quoted By:

>>11256796
It is not ?(36), it is 36*?(36), which is equal 36!

Anonymous

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Anonymous Fri 27 Dec 2019 08:49:13 No.11256809 Report

Quoted By: >>11259654

>>11256768
stoners OUT

Anonymous

Anonymous Fri 27 Dec 2019 08:55:19 No.11256818 Report

Quoted By: >>11257185 >>11257198

>all these attempts and nobody just uses the definition of the gamma function

Anonymous

Anonymous Fri 27 Dec 2019 09:23:03 No.11256846 Report

Quoted By:

$\int_0^\infty \frac{ e^{-x} x^{(c+d)-1} } { \Gamma(c) } dx = \frac{ \Gamma(c+d) } { 2\, \Gamma(c) } = \prod_{k=0}^{d-1} (c+k)$

$d=2, c=6*6$

$\frac{1}{2}\int_0^\infty \frac{ e^{-x} x^{ 6*6+1 } { \Gamma(6*6) } dx = \tfrac{1}{2}6*6*(6*6+1) = 666$

Anonymous

Anonymous Fri 27 Dec 2019 09:24:11 No.11256847 Report

Quoted By:

$\int_0^\infty \frac{ e^{-x} x^{(c+d)-1} } { \Gamma(c) } dx = \frac{ \Gamma(c+d) } { 2\, \Gamma(c) } = \prod_{k=0}^{d-1} (c+k)$

Consider $d=2, c=6*6.$

$\frac{1}{2} \int_0^\infty \frac{ e^{-x} x^{ 6*6+1} } { \Gamma(6*6) } dx = \tfrac{1}{2}\, 6*6\, (6*6+1) = 666$

Anonymous

Anonymous Fri 27 Dec 2019 09:25:36 No.11256849 Report

Quoted By:

$\int_0^\infty \dfrac{ e^{-x} x^{(c+d)-1} } { \Gamma(c) } dx = \dfrac{ \Gamma(c+d) } { \Gamma(c) } = \prod_{k=0}^{d-1} (c+k)$

Consider $d=2, c=6\cdot 6.$ , then

$\dfrac{1}{2} \int_0^\infty \dfrac{ e^{-x} x^{ 6\cdot 6+1} } { \Gamma(6\cdot 6) } dx = \frac{1}{2}\, 6\cdot 6\cdot (6\cdot 6+1) = 666$

Anonymous

Anonymous Fri 27 Dec 2019 14:21:24 No.11257185 Report

Quoted By: >>11257530

>>11256818
which is?

t. brainlet

Anonymous

Anonymous Fri 27 Dec 2019 14:27:26 No.11257198 Report

Quoted By:

>>11256818
Why would you do that when you can do factorial

Anonymous

Anonymous Fri 27 Dec 2019 14:51:14 No.11257219 Report

Quoted By:

this is the first one of these "you should be able to solve this" which isnt an open problem or batshit retarded

Anonymous

Anonymous Fri 27 Dec 2019 16:02:57 No.11257344 Report

Quoted By:

>>11256505
Why should I? Explain.

Anonymous

Anonymous Fri 27 Dec 2019 17:52:33 No.11257530 Report

Quoted By:

>>11257185
$\Gamma(n) = (n-1)!$ for $n\in\mathbb{N}$ is as much as you need to know to solve this
It's proper definition is
$\Gamma(z)=\int_0^\infty x^{z-1}e^{-x}dx, z>0$

Anonymous

Anonymous Fri 27 Dec 2019 18:22:19 No.11257582 Report

Quoted By:

>>11256505
something in terms of the gamma function

Anonymous

Anonymous Fri 27 Dec 2019 18:54:01 No.11257647 Report

Quoted By:

i don't know what a big Gamma means bros....

Anonymous

Anonymous Fri 27 Dec 2019 19:00:11 No.11257655 Report

Quoted By: >>11257661 >>11258039

>>11256505
Wow, unbelievably cringe. This is basically like writing $\frac{1}{e} \lim_{n \to \infty} (1 + 1/n)^n . [/math] It's literally not math, it's just testing whether you've seen the gamma function before. Why are people like this? Is this what normies honestly think advanced mathematics is?$

Anonymous

Anonymous Fri 27 Dec 2019 19:02:24 No.11257661 Report

Quoted By:

>>11257655
Fuck me, obviously meant $\frac{1}{e} \lim_{n \to \infty} (1 + 1/n)^n .$

Anonymous

Anonymous Fri 27 Dec 2019 19:55:29 No.11257765 Report

Quoted By:

>>11256505
Doesn't look too complicated.

Anonymous

Anonymous Fri 27 Dec 2019 21:50:21 No.11257945 Report

Quoted By: >>11257953

lads, im in physics 2nd year and I havent run into the gamma function yet. I found the definition but the integral to find gamma(36) looks like there is some easier way. Where do I start to make sense of the gamma(36)?

Anonymous

Anonymous Fri 27 Dec 2019 21:53:46 No.11257953 Report

Quoted By: >>11257965

>>11257945
oh nvm I see, so gamma(n)=(n-1)! then 36gamma(36)=36! okay lemme try this shit bois

Anonymous

Anonymous Fri 27 Dec 2019 22:01:21 No.11257965 Report

Quoted By:

>>11257953
wtf I got 1/6

Anonymous

Anonymous Fri 27 Dec 2019 22:46:54 No.11258022 Report

Quoted By:

I got 1/2, for some reason my gamma(36) canceled out.

Anonymous

Anonymous Fri 27 Dec 2019 22:57:31 No.11258039 Report

Quoted By: >>11258254 >>11259035

$\int_0^\infty {\rm d}x \frac{6e^{-x}x^{37}}{12\cdot35!}=\frac{6}{12\cdot35!}\int_0^\infty {\rm d}x\,e^{-x}x^{38-1}=\frac{1\cdot37!}{2\cdot35!}=666.$
That was cute!
>>11257655
Nah, that's like a standard undergrad physics exercise warmup sheet.

Anonymous

Anonymous Sat 28 Dec 2019 00:09:19 No.11258201 Report

Quoted By:

>>11256562
have 6ex

Anonymous

Anonymous Sat 28 Dec 2019 00:41:57 No.11258254 Report

Quoted By:

>>11258039
My point is that it's basically just invoking the definition of the gamma function while using the same gamma function as one of the terms.
If someone saw this and asked, "I've never seen that gamma function down there, how do you define it?" you'd immediately realize how stupid the expression is.

Anonymous

Anonymous Sat 28 Dec 2019 00:49:51 No.11258268 Report

Quoted By: >>11258282 >>11258397

>>11256505
math brainlet, what is the symbol in the denominator and what does it mean

Anonymous

Anonymous Sat 28 Dec 2019 01:01:31 No.11258282 Report

Quoted By: >>11258397

>>11258268
it's an uppercase gamma and stands for (n-1)!

Anonymous

Anonymous Sat 28 Dec 2019 02:08:27 No.11258397 Report

Quoted By: >>11258436

>>11258282
>>11258268
gamma function is a continuous analog of (n-1)! and is equal to it at the integers

Anonymous

Anonymous Sat 28 Dec 2019 02:36:40 No.11258436 Report

Quoted By: >>11258449

>>11258397
neat. how the hell do you invent something like this and what would be the train of thought to come up with e to a negative power blah blah something and then boom, a continuous factorial?? would probably need iq>130.

Anonymous

Anonymous Sat 28 Dec 2019 02:48:24 No.11258449 Report

Quoted By:

>>11258436
Integration by parts. The guy who introduced it, Euler, was extraordinarily intelligent, as you suspected.

Anonymous

Anonymous Sat 28 Dec 2019 06:56:31 No.11258822 Report

Quoted By: >>11259376

>>11256562
>e^(-x) x^n
>already in the standard gamma function form
>change of variables into some weird form

are you retarded? its immediately clear its 1/2 * 37!/35!

Anonymous

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Anonymous Sat 28 Dec 2019 10:20:12 No.11259035 Report

Quoted By: >>11259607

>>11258039

Anonymous

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Anonymous Sat 28 Dec 2019 14:31:36 No.11259376 Report

Quoted By:

>>11258822
>are you retarded?
Well, it appears I actually am, but I'm also a high schooler and all I knew about the gamma function was that n!=?(n+1)=*the weird shit I turned the integrand into*

Anonymous

Anonymous Sat 28 Dec 2019 17:30:03 No.11259607 Report

Quoted By: >>11259644

>>11259035
>ignoring the ! sign

Anonymous

Anonymous Sat 28 Dec 2019 17:53:39 No.11259644 Report

Quoted By:

>>11259607
What do you mean you can't simplify the !s ?

Anonymous

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Anonymous Sat 28 Dec 2019 18:00:51 No.11259654 Report

Quoted By:

>>11256809

You just need to....relax...man...just...chill...man...

Anonymous

Anonymous Sat 28 Dec 2019 18:17:00 No.11259678 Report

Quoted By:

Just partially integrate it 37 times brainlets

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