Mathematics - 2014-09-01 (page 1 of 5)

who knows, buddy

Anthony

<3

Karl Kronenfeld

What interesting conjectures are you working on @MikeMiller?

@KarlKronenfeld It's conjectured that I'll pass quals in a month, but unproven

Karl Kronenfeld

Ah, good luck

12:27 AM

Well, I think I've got the key idea necessary

2:14 AM

greetings folks

Jasper Loy

4:06 AM

I am very irritated by XXX who keeps pinging people in chat to answer his math questions. But then again, it is his right to do so.

3

It is a beautiful September afternoon. Four more months to the new year!

By the way @robjohn what did you want to ask me?

r9m

@JasperLoy does XXX refer to someone with 3 letters in their username ? :P

Jasper Loy

@r9m Nope, lol.

I should spend the rest of this year learning LaTeX.

r9m

@JasperLoy why does it annoy you if someone asks for help with his math in a math chat room ? :o

Jasper Loy

@r9m Which is why I added the second sentence.

Actually I was referring to Vrouvrou.

5:48 AM

Hmmm, if I have a velocity vector - how do I find its speed :s?

$\alpha. \boldsymbol{v}$. Since, $\boldsymbol{v}$ is the direction, is $\alpha$ the speed?

Greetings @robjohn @r9m

Here are 2 interesting series to check

$$\sum_{n=1}^{\infty} (H_n-\log(n)-\gamma)^2$$

$$\sum_{n=1}^{\infty} (H_n-\log(n)-\gamma)^3$$

OK, let's add some more

$$\sum_{n=1}^{\infty} (-1)^{n+1} ((H_n-\log(n))^2-\gamma^2)$$

$$\sum_{n=1}^{\infty} (-1)^{n+1} (H_n^2-(\log(n)+\gamma)^2)$$

$$\sum_{n=1}^{\infty} (-1)^{n+1} ((H_n-\gamma)^2-\log^2(n))$$

I just created them.

6:06 AM

@GustavoMontano speed is the length, or absolute value of the velocity vector.

@Chris'ssis Hello :D

@Hippalectryon Hi

@Chris'ssis What is $k$ in hostimg.org/show-image.php?id=f3d6d65975d270010ba71fbe9cf536bc ?

@Hippalectryon the number of variables ...

@Chris'ssis I mean, it doesnt appear on the RHS

Is it true for all $k\in\mathbb{N}^*$ ?

6:11 AM

@Hippalectryon It should be $k$ in the right side (I need to check my papers).

Wait ...

@Hippalectryon Yeah, it is true for all $k\in\mathbb{N}^*$.

Ok thanks

@Chris'ssis Also in prntscr.com/4ijto2, was it meant to be $(-1)^{n+1}$ ?

@Hippalectryon Forget about that.

?

@Chris'ssis Does it not hold ?

@Hippalectryon It holds. That limit above is $1$.

@Hippalectryon I initially thought of a wrong version I posted somewhere.

What do you mean by $\mathcal{O}$ by the way ? Dominance or predominance ?

6:20 AM

Big O notation

In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the "error committed" while...

Ok :)

Btw i ordered the book :D

@Hippalectryon The sum you showed me is $\approx (2\log(2)-1)n$ and this can be written as $\mathcal{O}(n)$.

@Hippalectryon Good job! Which version? A hard copy or e-book version?

@Chris'ssis Hard copy, i should have it before next week

@Hippalectryon Does it take so long?

I'm in France :)

And they don't have a lot in stocks

So I guess it's imported from some place

6:23 AM

I see.

@Hippalectryon By the way, some days ago I worked on some limits you'd die for pleasure to see them. :-)

These ones will be in my book.

@Chris'ssis :D

* yum *

Is there a way to write sums of sums a more elegant way ? $\sum\limits_{n_1=1}^\infty\sum\limits_{n_2=1}^\infty\dots\sum\limits_{n_k=1}^\i‌nfty (-1)^{\sum\limits_{k=1}^nn_k}\cdot\frac{H_{\sum\limits_{k=1}^nn_k}}{\prod\limits‌_{k=1}^nn_k} =(-1)^n\int_0^1\frac{\ln^n(1+x)-\ln^n(2)}{x-1}$feels a bit heavy

@Hippalectryon Yeah, it is. By the way, replace $n$ in the right side by $k$.

How do I do that ?

$$\sum\limits_{n_1=1}^\infty\sum\limits_{n_2=1}^\infty\dots\sum\limits_{n_k=1}^\‌infty(-1)^{\sum\limits_{k=1}^nn_k}\cdot\frac{H_{\sum\limits_{k=1}^nn_k}}{\prod\li‌mits_{k=1}^nn_k} =(-1)^k\int_0^1\frac{\ln^k(1+x)-\ln^k(2)}{x-1}$$

@Hippalectryon I can't tell you more at the moment. ;)

@Chris'ssis Uh, what I meant is : is there some mathematica symbol to write sums of sums

6:32 AM

@Hippalectryon Well, I like the way I put things there. I wouldn't change that.

Ok :)

Just looking at prntscr.com/4ijx0y makes me think that the proof of the above is hard :c

@Hippalectryon Well, it depends on how you approach things. With a bit of inspiration, it's not that hard. I sent that somewhere to be published.

It's not that hard..... when you've done that for years xD

I barely know anything about Gamma, Polygamma, Li, Dirichlet functions...

@Hippalectryon For years? Are you joking, right? :-) Just look at the questions I asked 2 years ago or so on main.

Q: Compute $\lim_{n\to\infty} \left(\int_0^{\pi} \frac{\sin^2 n x}{\sin x} \ dx-\sum_{k=1}^n \frac{1}{k}\right)$

@Chris'ssis Well at least one year :)

I have some if your papers from late 2012 i think

That was two years ago

13

Compute the limit $$\lim_{n\to\infty} \left(\int_0^{\pi} \frac{\sin^2 n x}{\sin x} \ dx-\sum_{k=1}^n \frac{1}{k}\right)$$

:c

I'm not able to do that at all right now

6:39 AM

@Hippalectryon lol, I don't believe you. ;)

@Chris'ssis You even posted that comment prntscr.com/4ijy48

How do you expect me to know that xD

Is there a LaTeX command for Li ?

@Hippalectryon lol, you're funny now.

@Hippalectryon use \operatorname{text}

I've never ever heard of Catalan-Botez :c

@Hippalectryon See this one math.stackexchange.com/questions/73550/…

Btw if anyone can help me here

0

Q: Folding sheets of paper

You have $n\in\mathbb{N}^*$ sheets of paper with dimensions $a,b\in\mathbb{R}_+^*$ that can be folded as many times as needed. What is the set of lengths in $\left]0,\sqrt{a^2+b^2}\right]$ one can build ? Same question with $n\in\mathbb{N}^*$ sheets of papers with dimensions $a_n,b_n\in\mathbb{...

recreational-mathematics

6:44 AM

Interesting

Guys serious question, I need d help and I think people think I am trolling

I have two classes "Bundle" and "Faggot"

Can anyone think of a better name for "Faggot" (a bundle with specific properties)

@Chris'ssis I was in a store, toying with some towel, and then I started wondering what all the lenghts I could build with that towel would be :D

I'm totally serious. Faggot is not a word I want appearing in code documentation

@AlecTeal Why can't you rename those ?

@Hippalectryon :)))

6:47 AM

@Hippalectryon Bundle is widely used and already in use

I need a synonym for Faggot

:17442602 Please do not post it again. You need to let some spaces when you have such big expressions.

Oh sorry

You know a Bundle of data, it's a nice word and works well as it's a collection of a certain kind of data. However a Faggot of data, a function that excepts 2 faggots, stuff like Faggot* myFaggot = new Faggot; is not .... it's weird.

@AlecTeal But can't you rename it to any better name just for your question ?

@Chris'ssis prntscr.com/4ijzpb

Well I need an alternative word.

6:50 AM

What annoys me is that there is still some space on the left @Chris'ssis

@Hippalectryon OK, but I prefer my form of writing things. :-)

@AlecTeal English isn't my native language so I fear I'm not gonna be able to help :)

@Chris'ssis I'm trying to optimize space a bit in order to print less pages

@Hippalectryon OK :-)

Any idea how to recenter it ?

7:04 AM

Thanks @skullpatrol.

Thanks for asking :-)

@skullpatrol, one more question. I understand that if $\boldsymbol{r}(t)$ is the parameterisation of a curve then the tangent is given by $T=\frac{\boldsymbol{r}'(t)}{\Vert \boldsymbol{r}'(t) \Vert}$. Does the velocity follow the same definition? Or is it just the derivative?

@AlexTeal how about a group of data

Actually, that $T$ is the unit tangent.

I wonder why we work with unit tangents :s.

The velocity is the derivative.

7:16 AM

What are that sum's bounds (the one in the root) ? prntscr.com/4ik4m0

8:38 AM

Great grades overall. Discrete Mathematics: E

I literally didn't sleep studying for that exam

I hate it

:/

What kind of questions were there ?

Mindless applications of algorithms

anyway I need to celebrate my other grades

8:55 AM

* champagne *

celebrate good times

3

robjohn

9:11 AM

@Chris'ssis any idea of what they are?

@robjohn I'm sure all of them have nice closed forms.

@Chris'ssis prntscr.com/4iks63 isn't the denominator $n(n^2+3n+2)2^{n+2}$ ?

@Hippalectryon Yeah, it is. But I also posted the corrected version on channel.

I'm not always here :)

@Hippalectryon btw, do you make a collection with my questions? :-)

9:15 AM

Also, how did you get $A$ in the answer ?? I don't see it anywhere in the general solution

@Chris'ssis I do :D

I'm making a pdf, because I had like 30 screenshots

@Hippalectryon $A$ comes from Glaisher-Kinkelin constant.

@Chris'ssis I mean, why does it appear ? The general solution only has $\ln$ and $\Gamma$ and $G$

@Hippalectryon Ah, it's due to a special value of Barnes-G function.

Oh ok

$\displaystyle\;G(3/2) = \frac{\sqrt[24]{2 e^3 \pi^6}}{A^{3/2}}\;$ :D

Ugly :c

@Hippalectryon No, not at all. This is very beautiful.

mathworld.wolfram.com/BarnesG-Function.html

9:19 AM

I went there already :)

But $A=\underset{n\rightarrow\infty}{\lim}\dfrac{H(n)}{n^{n^2/2+n/2+1/12\cdot e^{-n^2/4}}}$ IS ugly eww

@Hippalectryon well, in math many things might look ugly at first sight, but when you're used to them, you realize that everything is of a divine beauty.

2

Have you seen this one? $$\int_0^{\large1/1^2} \left\{ \frac{1}{t} \right\}\,\mathrm{d}t-\int_0^{\large 1/2^2} \left\{ \frac{1}{t} \right\}\,\mathrm{d}t+\int_0^{\large 1/3^2} \left\{ \frac{1}{t} \right\}\,\mathrm{d}t-\cdots $$

@Chris'ssis But from an uninitiated point of view... uh ... it's like abstract art. I guess I have to study more :D

@Chris'ssis Nope, what does it equal ?

@Hippalectryon Well, you need to find this on your own. ;)

@Chris'ssis I guess i'll screenshot it like the others

I'll come back to it in some years

When i'm good enough :)

@Hippalectryon lol, if I could believe you ... ;)

9:24 AM

@Chris'ssis >:0

@Hippalectryon I think you know a lot of stuff.

I definitely won't have time this year because i'm in that kind of school for the second year en.wikipedia.org/wiki/…

And i changed schools for a way better one so from Tuesday onwards, I won't have as much time as before for myself

Lots of work

I guess i'll still be here to ask questions xD

And unfortunately we don't study fractional integrals :c

Interesting. In general I'm more tough with myself than any school in the world might be.

tough with myself ? (i've never encountered this expression before, what does it mean ?)

@Hippalectryon I'm mean I established high standards to me, very high objectives to reach. I f I publish a book of limits, series and integrals then I expect it should be the best one in the world. Maybe this sounds completely crazy for some, but not for me.

9:29 AM

@Chris'ssis Which is a good thing :)

@Chris'ssis I hope it will be !

It's not crazy :) i often feel the same when doing computer sciences

@Chris'ssis Btw, i've been wondering, where does your pseudo come from ??

@Hippalectryon That's not that important, believe me. ;)

I guess it isn't, even mine is totally random (I found it while browsing wikipedia) :D i was just wondering what 'chris' was referring to

@Hippalectryon my bro

Oh -__- that's logical then xD

10:23 AM

@Chris'ssis

@BalarkaSen

@Chris'ssis Did you see my solution to the limit?

@BalarkaSen Yeah, it's a great solution. You should come in our area of limits, series and integrals. :-)

=)

Thanks. But I'll think I'll keep it as free-time math.

Good.

10:25 AM

Also, deeply sorry about your dog.

I am glad that you came back.

@BalarkaSen Thank you. At any rate there is nothing I can do ... I'll be sad for a while, but the most important thing is to continue my work, otherwise I can lose much more than that.

Right.

@BalarkaSen I loved that dog at most.

I understand. I had cats once.

@MikeMiller mystical greetings

Aug 28 at 10:35, by Chris's sis

@skullpatrol I cannot afford that, I need to work hard on my results, I plan to publish an exceptional book, so I try to work as much as I can, less rest, less party. You know, to do such things it's hard since when you're about to create something big, you lose the support of the people you think would support you in such situations.

10:30 AM

@Daniel @skull... WAT

this is confusing

you lose the support of the people you think would support you in such situations uh ?

@skullpatrol Thanks! Much very hard work is needed! :-)

:D

Daniel Fischer

@BalarkaSen What have I to do with anything? What is it about anyway?

@Hippalectryon Well, that means that you spend a lot of time working on a project and some might not understand that, they might think you neglect them. There is a lot of work to do, I don't have time for parties, for usual talks, I need to work and publish my book.

10:32 AM

@DanielF look at skull's avatar.

@DanielFischer refresh your browser

@Chris'ssis That's sad

@Chris'ssis I never go to parties anyway xD

I'm either at home or at school

I'm always at home

Daniel Fischer

@skullpatrol Not an improvement in terms of image quality (or looks).

3

:D

10:34 AM

@skullpatrol You should have photoshopped it a bit :) add a santa hat

yeah

at least some distinctions are good

@Hippalectryon Never? Why never?

otherwise it's just too confuzzling

@Chris'ssis I don't have time

@Hippa rolls eyes

And you have time to chat here?

10:36 AM

* because i don't have friends * errno

.

@BalarkaSen I'm working at the same tame - and fyn i'm eating lunch atm

@BalarkaSen School only starts tomorrow for me

Hell starts tomorrow

I hate school

3

I love school

So much to learn

I love the self-education.

10:43 AM

I love any kind of education. Just not school.

robjohn

@JasperLoy It's okay... I was uncertain whether edit 3 was warranted. I have convinced myself that it is.

@Chris'ssis But it's kind of hard to educate yourself in maths, physics, chemistry, engineering sciences, english, french, research, computer sciences without the help of anyone to correct what you do

@BalarkaSen What's bad about school ?

Sush

@DanielFischer, let $g(t)=f(x+tz)$ be differentiable where $t$ is a scalar and $x,y\in \mathbb R^n$. Then how does $g''(t)=z'\cdot D^2f(x+tz)\cdot z$ hold?

@Hippalectryon Waste of time.

@BalarkaSen uh ?

How so ?

10:44 AM

@Hippalectryon I know, but this is the way I'm made as regards math.

@Chris'ssis Maths are ok to learn by yourself, but it's harder for other subjects

Especially languages

I could do lots of math while not in school attending the completely boring lectures

Who cares about languages

@BalarkaSen That's because you have a bad school :c

i am good enough at eng.

Daniel Fischer

@Sush $z'$ means the transpose there. Chain rule, twice.

10:45 AM

I got a B in english

@BalarkaSen If I hadn't learnt english I wouldn't be here

don't say THAT WOULD BE A GOOD THING

That would be a good thing

do I get a prize now?

-_________-

Sure

Sush

@DanielFischer, ok!

Lenny face

Here is your prize ( ͡° ͜ʖ ͡°)

10:46 AM

^_^

@Hippalectryon I'm aware that here I usually make mistakes while typing, but if you hear me talking you might barely figure out I'm from Romania. I learned English alone, without any teacher. If I struggle a bit, I'm definitely sure I can write things correctly almost all the time.

@Chris'ssis But you're way older than me aren't you

At least twice as old

@Chris'ssis Please speak English we don't understand what you are saying.

I guess

tee hee