@meg_1997 Did they help you?

Hey, you write uncommonly fast Gigili.

I have no idea how editing works, is it bad to edit while someone else is and is there any way to avoid that?

Does anyone know how complex numbers are related to probability ? My friend typed 100 choose 50 into wolfram alpha and aquired this

Editing your question on the main site?

yes

Or what?

@Jordan Unfortunately there's not much of a way to avoid that. Unless there are measures in place I was not informed of.

@N3buchadnezzar Well, probability is related to combinatorics, and combinatorics is related to special functions, and special functions are related to complex analysis.

That's pretty much your explanation right there.

Makes me want to learn more =)

I guess the combinatorics is related to gamma, which is related to beta, which is again related to complex analysis... Hmm

a somewhat less circular answer is that factorials can be expressed in terms of the gamma function

the one you're looking at just depends on the binomial expansion and basic contour integration rules

because $-i=1/i$, and by $\frac{1}{2\pi i}\oint_\gamma z^mdz$ is $1$ if $m=-1$ and $0$ otherwise, with $\gamma$ the unit circle.

Gammas and betas are unnecessary.

Yikes, too many circles. I can't be bothered to solve this now.

hey

I remember an online pdf note about Collatz and topology / dynamical systems, that might be relevant.

ill google that thx

I'm not sure I have ever gotten 50+ views without someone even attempting to answer lol

ah, it was math.moravian.edu/mfraboni/math/LongHonors.pdf, also 2-adic

thx I will take a look a this

this question turned out to have great answers

very thorough. hope i get something like that =P

found this

Nice answer @robjohn.

@Gigili which one?

$S_1$, $S_2$ and $S_3$.

cecm.sfu.ca/organics/papers/lagarias/paper/html/node1.html

this is pretty good

lagarius apparently really likes this problem =P

@Gigili Ah, thanks :-) I just added an explanation of how the construction was derived.

@anon I think it's a crummy question. But yeah.

A question arising from meta: Is there a more refined word for "circlejerk"?

self-congratulatory I guess

That's what I was thinking! But it doesn't imply as much. You can be self-congratulatory on your own.

echo chamber, elitist or snobbish are related I suppose

@DylanMoreland That's why the question has more stars than upvotes :)

that's always a sign the question is being starred more for the answers than anything

BRB. Dog and I are going to the park. Beautiful day in Ann Arbor.

@anon What is the relationship between "stars" and "up-votes"?

A star signifies a user who has favorited a question - often because they think it's a good question, or they want to get back to the question and its answers at a later date when they have more background, or they simply think the answers are good. Upvotes also come for a number of reasons - being clear, well-researched, interesting, sympathy for the OP, or something someone else wants to know as well. Sometimes upvotes and stars intersect, sometimes they don't.

@skullpatrol stars : comments :: upvotes : answers/questions

stars > up-votes

stars < up-votes

@DylanMoreland Is Dog a name or simply a classification?

Hey Dog, get out of the trash!

Dog could also be a metaphor ;-)

@Gigili It looks as if that question (and therefore my answer) will get little attention.

@anon they have parties every Friday night; that's how

@robjohn That's sad. It's not your first answer which gets little attention even though you put much effort into it.

@Gigili The harder the question is, the less attention it gets, for the most part.

@anon racing for lhf?

the trig question andre got

Now that I know your email address @anon, I'm going to do something evil.

one of many :)

I've already seen goatse, bme pain, tubgirl, 2 girls 1 cup, whathaveyou.

We'll see.

2 cups 1 girl.

@JasperLoy Indeed.

@JasperLoy ;-)

Eh, okay.

Most people who foray into the wild world of internet comment threads ...

I suppose "online internet" is redundant.

I read the title of this and was having a panic attack for a moment

@anon Hahaha that's a funny thing to ask.

@anon LOL "intellectual masturbation"

@PeterTamaroff intellectual masturbation

$E = mc^2$ is the most famous equation of the 20th century

@anon I was acquainted with "intellectial orgasm" but not that one!

surely 1+1=2 is more famous

not

Oh crap, how do you circumvent the too-few characters thing without LaTeX!?

Fame is judged by popularity here :)

Need to find me some zero-width characters.

I was too lazy, just said (extra characters in parentheses)

In other news, I am officially out of notebooks, and am now using printer paper.

(until further notice)

@JasperLoy How do you get your avatar to fly in and out?

@anon I always use printer paper!

Then I perforate and put 'em in a binder.

@anon I'm trying to groke this:

Given that $d \mid a $, then $$\Large \sum_{d \mid a}\sum_{b \mid \frac a d}= \sum_{b \mid a}\sum_{d \mid \frac a b}$$

I guess the english is messing with me now: "for $b$ only runs through positive divisors of $a$, and to every such $b$ there corresponds exactly to those $d$ for which $d \mid a$, and in fact for which $db \mid a $, that is, for which $d \mid \frac a b$."

@robjohn Look what I found :D

@skullpatrol "subjective and argumentative" :-)

@robjohn Indeed. Shound I add a link to it in my post?

@PeterTamaroff It is just summing over every factorization of $a=bd$.

@skullpatrol I don't see why not.

@robjohn The words got me dizzy. How woudl you rewrite that?

@robjohn I don't want "them" to close my post too :(

@PeterTamaroff I'm sorry, it is summed over every factorization of every divisor of $a$

That is $bd|a$

@PeterTamaroff That is pretty much how I would write it: the sum runs over all $b$ and $d$ so that $bd|a$

@robjohn Remember they almost suspended me for spamming the "textbook answer."

@robjohn No, his name is Rico. I'm probably missing a "the".

@DylanMoreland Ah, Rico is a nice name for a dog.

@anon Hah!

@robjohn It was just on the adoption papers. Rico Suave.

@robjohn I posted your answer on my blog here

@AméricoTavares Thanks for the link :-)

@robjohn I've left it in English

@JasperLoy I pasted a copy of the "textbook answer" into each answer's comment box.

@robjohn I've wanted to share it with my readers.

@JasperLoy To get their opinion.

@JasperLoy Me too :(

@skullpatrol I could see how that would be considered spam.

@robjohn I do too, now :(

@skullpatrol but you are quitting?

@robjohn Yes, all of my rep points are offered in the bounty to this question.

@skullpatrol I think the bounty points disappear if you delete your account.

as well as all the points from your other votes.

@robjohn I'll just leave my account dormant.

@skullpatrol Is there a reason that you're leaving?

@robjohn Time management. BTW I added two links to my question.

@skullpatrol There are probably other links, too. I am sure this has been brought up many times before.

True that.

there aren't any real tricks I can use to manipulate $(lnx)^2$ to make it easier to integrate is it? I am trying to do $x^2 (lnx)^2$

@Jordan how about the substitution $e^u=x$?

I did it another way, I did integration by parts like 3 times

not sure if this is correct yet

@Jordan Integration by parts will handle it, too.

It is just really long, was hoping there was a simpler method

hmm I am way off from the books answer, for differential equations trying to find a solution for a specific input will there be more than one answer?