Mathematics - 2012-07-24 (page 1 of 3)

$S^1$ consists of stuff like $e^{i\theta} = \cos \theta + i\sin\theta$ for $\theta \in \mathbb R$. $SO(2)$ has stuff like $\begin{pmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{pmatrix}$.

And, well, there's a reason I used $\theta$ in both places.

BenjaLim

@HenryT.Horton Now that I call a smart arse.

Henry T. Horton

No, do it your way :)

BenjaLim

@HenryT.Horton Why did you remove that?

the determinant map is surjective

Dylan Moreland

12:17 AM

Both of the conditions ${}^tAA = I$ and $\det A = 1$ are closed, yeah.

Henry T. Horton

Yeah I left out the orthogonal condition

BenjaLim

@DylanMoreland wait I don't get the bit on the orthogonal condition

Henry T. Horton

But $F(A) = A^T A - I$ can be shown to be continuous, so $\mathrm{O}(n) = F^{-1}(\{\text{zero matrix}\})$ is closed

And the set $S = \det^{-1}(\{1\})$ is closed

BenjaLim

yes

Henry T. Horton

So $\mathrm{SO}(n) = \mathrm{O}(n) \cap S$ is closed

BenjaLim

12:21 AM

intersection of two closed sets is closed

Hmmm I need to get used to thinking about matrices this way

Henry T. Horton

That is a true fact!

BenjaLim

I should go and prepare for class at 11 now

Thanks @DylanMoreland @HenryT.Horton

Henry T. Horton

No

Dylan Moreland

Implicit function theorem is a good thing to learn, by the way.

Henry T. Horton

You should be able to deduce that a element of $\mathrm{O}(2)$ has the form $\pmatrix{a & b \\ -b & a}$. Then the determinant $1$ condition for it to be in $\mathrm{SO}(2)$ says $\mathrm{SO}(2)$ is the set of all $a, b \in \Bbb R$ such that $a^2 + b^2 = 1$, i.e. it's a circle

Gigili

12:26 AM

takes notes

Henry T. Horton

Hey Jiggly.

Gigili

Hullo.

Henry T. Horton

It doesn't seem that you are registered for this class. I'm going to have to ask you to leave before I get campus security involved.

Gigili

Go call the police, I took notes long ago and am ready to leave. Not that your lines are noteworthy, ish.

Henry T. Horton

Please don't leave, everyone else walked out.

I won't get tenure if everyone drops my class.

Gigili

12:31 AM

whistles

If you insist ...

Henry T. Horton

I'm not insisting anything. I don't want to pressure you.

Gigili

Well, there's this transcript thingy, I let the readers be the judge.

robjohn

@PeterTamaroff somewhat... did you have a guess?

Henry T. Horton

Is there an exact answer, Roberto?

robjohn

@HenryT.Horton There is an exact, closed form answer in terms of common constants.

Hints?

Frank Science

12:47 AM

@HenryT.Horton Which problem are you talking about?

robjohn

55 mins ago, by robjohn

Here is a cute problem: $\displaystyle\sum_{k=2}^\infty2^{-k}\tan(2^{-k}\pi)$

Peter Tamaroff

@robjohn OH! Cauchy condensation?

Frank Science

Do you think it expressible?

robjohn

@PeterTamaroff No, that only tests for convergence, it doesn't tell you to what it converges.

10 mins ago, by robjohn

@HenryT.Horton There is an exact, closed form answer in terms of common constants.

Peter Tamaroff

@robjohn Well, but it certainly does, and it gives bounds in terms of the uncondensed series.

I'm just going with $\pi$. Whatever.

=)

robjohn

12:57 AM

@PeterTamaroff True, it does give you bounds.

@PeterTamaroff Have you tried summing it? It converges very quickly.

Peter Tamaroff

@robjohn I haven't

Frank Science

0.31831

robjohn

@PeterTamaroff Think about $\cot(x)-\tan(x)$ and how it might be simplified.

@FrankScience Yes, so the answer is not $\pi$.

Peter Tamaroff

@robjohn OK. $2 \cot(2x)$

I see.

robjohn

@PeterTamaroff close, but not quite

Peter Tamaroff

1:06 AM

1 hour ago, by Peter Tamaroff

@robjohn Have you tried a duplication formula?

I didn't pay many attention.

Let me retry.

robjohn

@PeterTamaroff look at the numerator and denominator

Frank Science

$\tan\alpha=\cot\alpha-2\cot2\alpha$ and telescoping.

robjohn

@PeterTamaroff That's correct!

@FrankScience telescoping to what? :-)

Henry T. Horton

$1/\pi$

robjohn

@HenryT.Horton and how?

Frank Science

1:12 AM

$\lim_{n\to\infty}2^{-n}\cot 2^{-n}\pi$.

Peter Tamaroff

Jonas Teuwen

Hello boyos! All bugs which I have found are... fixed!

robjohn

@anon: wekcome back

Peter Tamaroff

@FrankScience You ruined it.

robjohn

@FrankScience indeed !

Jonas Teuwen

1:12 AM

@PeterTamaroff Looks like my hair this morning.

But my beard is bigger.

Henry T. Horton

$$\sum_{n=2}^\infty 2^{-n} \tan( 2^{-n} \pi) = -\frac{1}{2} \cot \frac{\pi}{2} + \lim_{n \to \infty} 2^{-n} \cot(2^{-n} \pi) = 0 + \frac{1}{\pi}$$

Frank Science

Another approach?

robjohn

@HenryT.Horton That's it

Peter Tamaroff

It is clear the $^{-1}$ in my previous answers wasn't rendering.

robjohn

@FrankScience do you have another approach?

@PeterTamaroff Ah, yes ;-)

Peter Tamaroff

1:16 AM

@robjohn Where did this arise, then?

robjohn

This problem came about when I was working out a way to do $\sum\limits_{k=1}^\infty\frac1{k^2}$

The function $\pi\cot(\pi z)-2\pi\cot(2\pi z)$ has poles at the odd integers with residue $1$

Peter Tamaroff

@robjohn Sick! Why would you want to do series?

@robjohn OK.

robjohn

and I worked out that that was $\pi\tan(\pi z)$

Peter Tamaroff

So?

Does this integral even make sense? $$\int\limits_{ - \infty }^\infty {\frac{{dx}}{{\sqrt {{k^2} - {x^2}} }}} $$

robjohn

@PeterTamaroff Then you can use residues and the function $\frac1{z^2}$ to get the sum of the series.

Peter Tamaroff

1:19 AM

@robjohn Cool.

Residue theory is badass.

robjohn

not outside of $[-k,k]$

Peter Tamaroff

math.stackexchange.com/questions/154816/…

robjohn

@PeterTamaroff it is wonderfulness

Jonas Teuwen

Too little residues for my distributions.

robjohn

@PeterTamaroff actually you could compute the outer parts as a complex number

@PeterTamaroff but it doesn't converge unless you consider it a Principal Value and take the sign of the radical opposite on both sides.

Peter Tamaroff

1:22 AM

@robjohn I see,

robjohn

That is a forward reference :-)

@PeterTamaroff The integral from $-k$ to $k$ is $\pi$ I believe

Peter Tamaroff

@robjohn Yes, just some $\arcsin$ery does it.

robjohn

@PeterTamaroff just seeing if I could do it in my head.

only two substitutions

Off to run some errands and take the dog to the park. We have company over for dinner, so I won't be back for about4 hours

Frank Science

1:39 AM

@robjohn What about $\tan z=\sum_{n\ge0}T_nz^n$?

Incidentally, like Knuth, I would prefer to use pencil rather than pen.

CLarue

2:01 AM

The primary reason why I prefer computer to pencil is that I don't accidentally erase half of the line above (I write small).

Frank Science

You cannot always use computer.

CLarue

Yes, but that does not change my preferences.

Peter Tamaroff

I just like the PC because of the templates and Ctrl+V Ctrl+C

Frank Science

PC is scratch paper?

Peter Tamaroff

@FrankScience Personal Computer!

Frank Science

2:08 AM

@PeterTamaroff I meant that you use PC as scratch paper?

Peter Tamaroff

@FrankScience Oh. Well, sometimes.

Frank Science

@PeterTamaroff I only use substantial scratch paper or my brain.

Peter Tamaroff

@FrankScience I don't like to waste paper. I don't have much and I need it.

Frank Science

@PeterTamaroff But there are some calculations I cannot work on computer.

Peter Tamaroff

@FrankScience Don't you have MathType of something of the sort?

Frank Science

2:13 AM

@PeterTamaroff No longer.

Peter Tamaroff

@FrankScience Why no longer?

Frank Science

@PeterTamaroff No longer do I use Windows.

Peter Tamaroff

@FrankScience What are you using now?

Frank Science

@PeterTamaroff There are many recyclable thing, such as advertisement with only one page printed.

@PeterTamaroff Newspaper is sometimes available.

Chuck Fernández

whats up nerdizzles

from the big bang theory (not offending)

anon

2:26 AM

up is the local outward normal of a surface

Peter Tamaroff

@ChuckFernández Say fo shizzle to my nerdizzles!

robjohn

@anon I tried that and fell down when I got to a wall.

Frank Science

WHAT IS THE BIG BANG THEORY?

robjohn

@FrankScience A very funny TV show

off to pick up dinner. bbl

Frank Science

@robjohn OH, I DO NOT LIKE THE TV SHOW.

CLarue

2:43 AM

Do you have caps lock on because you do not have to use the Shift key to start a sentence and type proper nouns?

anon

<Khassaki> HI EVERYBODY!!!!!!!!!!
<Judge-Mental> try pressing the the Caps Lock key
<Khassaki> O THANKS!!! ITS SO MUCH EASIER TO WRITE NOW!!!!!!!
<Judge-Mental> fuck me

Zhen Lin

your backquotes don't work, for some reason...

anon

'parrently they don't combine with linebreaks

Mark Dominus

CAPS LOCK IS A GOOD WAY TO GET PEOPLE TO PAY MORE ATTENTION TO YOUR MESSAGES.

anon

what's an easy way to see that $\pi_1\otimes\pi_2$ is irreducible iff $\pi_1,\pi_2$ are irreducible? the $\implies$ direction I see by contraposition and distributivity of tensor products through direct sums, but I don't see the "only if" direction. (I'm think in $\Bbb C$.)

Mark Dominus

2:52 AM

ALL CAPS SUGGEST URGENCY AND IMPORTANCE.

anon

CRUISE CONTROL FOR COOL

Mark Dominus

actually my computer does not even have a caps lock. I had to type that with my finger on the shift key.

Peter Tamaroff

Topologists! I need your help in proveing $\operatorname{int}(A\cap B)=\operatorname{int}(A)\cap \operatorname{int}(B)$

I have the proof that $ \overline{A\cup B}=\overline A \cup \overline B$

Maybe I can mimic some of that.

Mark Dominus

The first thing that comes to mind is that the interior of $X$ is the union of all open sets contained in $X$.

And then use De Morgan's law or something.

I hope that wasn't too much of a spoiler.

Peter Tamaroff

I'm writing something by myself. THen I'll see that

Mark Dominus

3:05 AM

I tend not to be cautious about answering questions addressed to "topologists" since I am not a topologist.

anon

if you're working with a metric definition of interior, proving inclusion in both directions should be straightforward

Peter Tamaroff

@anon I'm on da topological spaceshizzles now.

I have proved that if $x\in \operatorname{int}A\cap \operatorname{int}B$ then $x\in A\cap B$

That is a start.

anon

Are you familiar with $\mathrm{int}(S)=X\setminus(\overline{X\setminus S})$ and $X\setminus (A\cap B)=(X\setminus A)\cup(X\setminus B)$?

(when $A,B\subseteq X$)

Peter Tamaroff

Yes!

anon

then $$\mathrm{int}(A\cap B)=X\setminus(\overline{X\setminus (A\cap B)})=X\setminus(\overline{X\setminus A}\cup\overline{X\setminus B})=X\setminus(\overline{X\setminus A})\cap X\setminus(\overline{X\setminus B})$$

Mark Dominus

3:11 AM

Good night, gentlemen.

And ladies, if any are present.

Peter Tamaroff

@anon Sweet

Henry T. Horton

Ladies? Where?

If only I knew some girls... a girl...

Frank Science

@CLarue I did not have caps lock on. I just keep pressing Shift.

Peter Tamaroff

@anon That is the set theoric stuff I want to get more used to using.

Frank Science

@anon Reference?

anon

3:17 AM

your google-fu is weak

@PeterTamaroff distributivity is your everlasting friend

Frank Science

googlability?

Peter Tamaroff

@anon Well, and mostly using all together. Getting the big picture.

anon

google-fu refers to one's ability to research and find sources on the internet, typically via search engine functionality specifically. just google the convo I posted and you'd find bash.org.

@PeterTamaroff every single step in the derivation was distributivity here. :) how complements distribute through unions and intersections, how closures distribute through unions (in order to show how interiors distribute through intersections)

Frank Science

I googled and entered a website not appropriate for adolescent/children, therefore I closed that page immediately.

Henry T. Horton

im 12 and what is this

anon

3:21 AM

are you an adolescent/child?

Frank Science

not bash.org

anon

oh

ie porn

(not to conflate with "porn involving internet explorer," ye avid 34ers)

Peter Tamaroff

@FrankScience How old are you?

@anon Well, yes, but as you note you did use other stuff. Whatever. Let me hate myself for a while.

Frank Science

@PeterTamaroff This sentence suddenly reminds me of caution on avoiding discussing age in western country.

Peter Tamaroff

What?

What do you mean by "caution on avoiding discussing age in western country."?

Frank Science

3:28 AM

@PeterTamaroff Our teacher told us that we should avoid discussing the age with westerners.

Peter Tamaroff

@FrankScience I'm a little baffled by the constant distinction of "east" and "west".

Henry T. Horton

I'm Japanese, can you tell me?

Peter Tamaroff

I'm in Argentina. I don't give a rat's ass about the "east" or the "west".

anon

discussing age in a chatroom shouldn't be a problem unless: (1) you are in an unfriendly environment, (2) you have a stalker, (3) you are underage, (4) you simply don't want people to know how old you are. you have no social obligation to discuss it, but conversely there should be no problem in this situation if you want to. also, "westerners" is a rather broad category of people.

I watch some anime, can I be Japanese?

Henry T. Horton

Gaijin

anon

3:33 AM

:(

Peter Tamaroff

I remember watching Ranma as a kid.

Frank Science

It's famous for Atman?

Peter Tamaroff

@FrankScience The boy that turned into a redhead when put into cold water.

Frank Science

@PeterTamaroff I cannot get a clear picture.

Peter Tamaroff

anon

3:37 AM

I liked: ghost in the shell, samurai champloo, death note, monster. Many others I like purely out of nostalgia (eg dragonball z).

Peter Tamaroff

DBZ was pure awesome.

Specially DBZ GT

Henry T. Horton

DBZ nostalgia is the best

Wtf DBGT? Get out

anon

GT = nope

Peter Tamaroff

@anon Whaaa....?

I'm leaving now....

Bye byes.

anon

later

Peter Tamaroff

3:39 AM

@HenryT.Horton Expect toplogy questions tomorrow!

Henry T. Horton

Good, I'll take one of my vacation days tomorrow.

anon

I hope @PeterTamaroff knows "get out" is a figure of speech.

Henry T. Horton

GET OUT is a way of life

anon

do you know rep thry Henry?

Henry T. Horton

No I'm just a middle schooler

Frank Science

3:43 AM

@HenryT.Horton And you participate in Mathematics Olympiad?

Henry T. Horton

No I'm not smart enough...

@anon What representation theory are you looking at currently

anon

wait, do you know about braid groups? I think you know about algebraic topology

Frank Science

@HenryT.Horton I meant Mathematics Olympiad, not National Mathematics Olympiad.

anon

@HenryT.Horton just some basic stuff. in some chap 1 notes there was a proof that the tensor products of two irreducible reps is irreducible (everything in $\Bbb C$), but I couldn't understand it

Henry T. Horton

@anon I saw the Burau representation at a conference talk...

anon

3:47 AM

eh. I ask because I had an error in a braid group question I answered, and while I could just alter the example I gave I wanted to know more general theory behind ameliorating the sort of error I had

Frank Science

Your middle school is teaching representation theory?

anon

wooooooooosh

Frank Science

@HenryT.Horton ?

Henry T. Horton

Last year we did

This year is Langlands correspondence

Frank Science

Oh, astonishing.

anon

3:50 AM

Reminds me of Ilya and Rajesh discussing Galois.

Frank Science

In our school, no further mathematics was taught.

Dan M. Katz

4:01 AM

Hey guys...I'm reading through "Baby Rudin" and I'm currently on the chapter on the Riemann-Stieltjes Integral. I'm having some trouble finding the motivation for the generalization from the Riemann integral to the more general Stieltjes case. Any pointers?

anon

it allows you to express many number-theoretic sums in calculus terms and thereby allow useful calculus-like manipulations (like by-parts and substitution). personal example

also, your name sounds familiar, can't pin down how though

Dan M. Katz

Haha do you go to Stevens?

anon

nope

Dan M. Katz

Where are you from, if you don't mind me asking?

anon

Nebraska (USA)

Dan M. Katz

4:08 AM

Haha doubtful then. I've lived in New Jersey all of my life.

anon

4:46 AM

well let's see here. every subspace of $V\otimes W$ should be a direct sum of tensor products of subspaces of $V$ and $W$. Say $U\subset V\otimes W, U=\bigoplus_{i}V_i\otimes W_i$. If $\pi_1,\pi_2$ are irreducible and $U$ is an invariant subspace, then each $V_i$ and $W_i$ is a subrep of $V$ and $W$ resp. and so is $V$ or $0$ or $W$ or $0$ resp.; tensoring with $0$ is annihilation so the only invariant subspaces are $0$ and all of $V\otimes W$.

no, that's not right, we can't say each $V_i,W_i$ is a subrep. drats.

picking $v\in V,w\in W$, $\langle \pi_1(G)v\rangle=V$ and $\langle\pi_2(G)w\rangle=W$ for any nonzero $v,w$, so clearly any nonzero pure tensor in $V\otimes W$ will span every pure tensor under the linear action.

anon

6:24 AM

Hmm, we can write an invariant $U\subseteq V\otimes W$ as a direct sum of complementary invariant subspaces $$U=\bigoplus_i \left\langle(\pi_1\otimes\pi_2)(G_1\times G_2) \sum_j v_{ij}\otimes w_{ij}\right\rangle.$$

robjohn

6:41 AM

Please Read: Chat Rules

4

user19161

@robjohn Hey! Do you pin this every week?

anon

more like every month

robjohn

@JasperLoy whenever it falls off the board

anon

or biweekly, I can't remember

user19161

@anon Yeah, I can't figure out which n for 7n days where n goes from 1 to 4.

anon

6:45 AM

:)

robjohn

@JasperLoy most likely not $3$

user19161

@robjohn Yeah, the real world prefers even numbers to odd numbers somehow.

robjohn

@JasperLoy at least things that go into evenly ($1,2,4\mid4$).

David Wheeler

odd numbers are...well, odd

robjohn

@DavidWheeler $1$ is the oddliest number

anon

6:50 AM

2 is the oddest prime

user19161

Yeah, 1 is the only positive integer that is neither prime nor composite.

user19161

So what happens when one tries very hard to solve a research problem but fails, or finds out that someone else just solved it a month ago?

robjohn

@JasperLoy 5 is both prime and composite (depending on whether Gauss or Rational)

user19161

So it seems it can be hard to make a living out of mathematical research.

robjohn

@JasperLoy I think one generally drinks heavily.

user19161

6:54 AM

@robjohn Haha, I am having coffee now.

robjohn

@JasperLoy I am having tea

user19161

@robjohn Maybe Jonas is having whisky in his sleep now, hehe.

David Wheeler

(1+2i)(1-2i)?

robjohn

@JasperLoy sleep drinking?

@DavidWheeler $1-2!^2$

David Wheeler

(that was supposed to be read: "five"?)

trying to parse your reply: one minus two! (emphatic, see reference number two)

Zhen Lin

7:02 AM

There are FOUR lights!

David Wheeler

that is not your father's oldsmobile

anon

I have no idea what's going on.

David Wheeler

Zhen Lin made a reference to Star Trek (Next Generation, i think)

to which i countered with a twist on a general motors advertising campaign

it's like a geometric series....the first reply kinda sorta makes sense, the second reply is a lot more goof-ball, and the third reply is totally out of the ballpark

i'm pretty sure you understand such things

anon

par for the course

David Wheeler

eventually the conversation will become unbounded, and we can start over

Old John

7:08 AM

Good morning

David Wheeler

@OldJohn technically, yes, it is morning, here. and it's good. so...yes. hi there!

anon

7:39 AM

Aha! Character theory! $\langle\chi_\pi,\chi_\pi\rangle_G=1$ iff $\pi$ is irreducible, and so $\pi_{1,2}$ irreducible implies $$\langle\chi_{\pi_1\otimes\pi_2},\chi_{\pi_1\otimes\pi_2}\rangle_{G_1\times G_2}=\langle\chi_{\pi_1}\chi_{\pi_2},\chi_{\pi_1}\chi_{\pi_2}\rangle_{G_1\times G_2}=\langle\chi_{\pi_1},\chi_{\pi_1}\rangle_{G_1}\langle\chi_{\pi_2},\chi_{\pi_‌2}\rangle_{G_2}=1.$$ Glad that's over with.

narayanpatra

8:10 AM

i m in urgeny to solve to questions on probability. any one interested to help?

user19161

@narayanpatra You should post on the main site for more people to see. That way you get the most help.

anon

just state the question

narayanpatra

0

Q: Random variable events and its probability distribution

Identify the random variable in each of the experiments and the probability distribution followed by the variable. Also find the expected value of the random variable. a)Number of print mistakes in a text book are being estimated. b)200 cars are expected to arrive at inspection station during c...

and math.stackexchange.com/questions/174551/…

i m pretty weak in probability

user19161

...

narayanpatra

and tomorrow my exams are scheduled

will be a gr8 favor to me if any one solves these two

user19161

8:14 AM

@narayanpatra If your exams are tomorrow and you are so weak, you should study the theory first instead of working on examples. And I forgot all my probability, sorry.

narayanpatra

@Jasper: Nice suggestion bro, but little time is there for me to study. solution for these two questions will help me a lot.

user19161

@narayanpatra The time you spent posting here you could have spent studying, and you might have finished reading by now.

user19161

Doing these examples may not help you solve the problems you will meet tomorrow on the exam.

narayanpatra

Chances are very high that I will get this question in my exam. and my further study do not involves statistics.

user19161

Good luck for tomorrow, but note that this is not the right way to learn mathematics.

user19161

8:21 AM

@narayanpatra Chances are very high that you can finish studying these topics before the exam...

user19161

Morning @jonas! Have a nice day!

Jonas Teuwen

Hi.

narayanpatra

haha. I also think so. I have to study it myself.

Old John

@JonasTeuwen Hi there

user19161

@narayanpatra Yes, you need an attitude change to make progress.

Jonas Teuwen

8:26 AM

I need to call the doctor, stressy 8-).

user19161

@JonasTeuwen OK, do whatever you have to. There can be miracles when you believe.

Jonas Teuwen

Sure 8-).

user19161

@OldJohn Hi there. Now we have a chain of hi's.

Old John

@JonasTeuwen What is stressing you out today?

Jonas Teuwen

Bloody monkey, why does the mofo go on a holiday! 8-)!!!

narayanpatra

8:31 AM

@JasperLoy na, I don't think. I have to change my attitude. many times we require a stop gap arrangement, and its same here. I m pretty good in many things which I love to do. stats is not what I am interested in. Its a compulsion from my college and I am just completing formalities.

user19161

@narayanpatra OK, if you need this kind of help you should be asking the people around you. SE is not really a site for solving your last minute problems.

user19161

@JonasTeuwen It's OK, I am here for you bro...

user19161

@jonas I did not see that.

user19161

@jonas OK I saw that.

Jonas Teuwen

Oh well.

Old John

8:37 AM

Planning to go and do a bit of hill walking while the weather is good - back later, folks

user19161

@JonasTeuwen I sent you a short email.

user19161

@OldJohn Enjoy the walk.

Old John

@JasperLoy Thanks - take care!

Jonas Teuwen

@JasperLoy Thanks :-).

Ilya

9:05 AM

@Jonas: hi

Jonas Teuwen

@Ilya Hi!

Ilya

@Jonas: so have you read it?

Jonas Teuwen

@Ilya No, I was too ill :-(. I will try to do today!

Ilya

oh no! ill? what had happened?

Jonas Teuwen

@Ilya I don't know.

ami

10:47 AM

How can I solve the third order differential equation with non-constant coefficient.

$$ \frac{1}{30} \frac{\partial ^3}{\partial x^3} S(x,y) - 2S(x,y)\left \{\frac{y^3}{(1-xy)^3}
+ \frac{1}{(1-x)^3}\right \} \\
~=\frac{24y}{1-y}\left \{\frac{1}{(1-x)^7} - \frac{y^5}{(1-xy)^7}\right \} $$

Jonas Teuwen

Whoah. Try with a computer.

ami

@JonasTeuwen with Mathematica?

robjohn

@ami Yeah, a numerical solution looks plausible.

Jonas Teuwen

For example...

ami

I tried with wolframalpha.com. It gave timeout :P

@robjohn thanks. how can I approach in case I want to solve it by myself.

Jonas Teuwen

10:52 AM

Learn more mathematics, I suppose. If you don't know how to begin you will fail I am afraid.

ami

@JonasTeuwen At university, I read only 2nd order and 1st order DEs.

@JonasTeuwen never come across third order DEs

Jonas Teuwen

If the $3$ would be a $2$, would you know how to solve it?

ami

Is it possible to reduce the order of 3 to 2 ?

@JonasTeuwen $y = c_1y_1 + c_2y_2$ -2nd order homogeneous eqn

Jonas Teuwen

I know. But you don't seem to know much about them then I think you should learn more first before you attempt this equation because it is quite hard (at a first glance).

And if you got them from a model you are required to solve you probably have done something wrong.

ami

@JonasTeuwen I am trying to find the average cost of median of 5 - Quick select using Generating function. This is the closed form equation which I want to solve.

@JonasTeuwen If you are interested, I can email you the paper which I am writing.

Jonas Teuwen

11:03 AM

I doubt you will get a closed form. Need to go now. See you later. Good luck, perhaps I can look at it later on.

ami

Sure.

Do you want the paper?

I am more interested in finding the coefficient of $[x^ny^i] in S(x,y)$

@JonasTeuwen I don't have PHD degree. I work for a software company.

@JonasTeuwen Take care.

BenjaLim

11:52 AM

@JonasTeuwen hey

Transcript for

$Mathematics$ Mathematics