Mathematics - 2015-11-10 (page 2 of 4)

Karim Mansour

05:00

yeah it is $(x_1,x_2) \in A_1 \times A_2$ such that $x_1 \in A_1 \ and\ x_2 \in A_2$

which is the same as above

user147690

Yeah so $x\in A_1\times A_2\times \cdots \times A_n$ means that $x$ is an n-tuple

Karim Mansour

yeah

which is same as mapping definition

yeah good I hate it when I confuse definitions sometimes

user147690

Yeah usually happens when I am tired

Karim Mansour

yeah exactly

next semester I shouldn't have as much heavy course load though, so it should be good

Remember me

05:17

what all the topics you have next semester @Karim?

Karim Mansour

algebraic topology and applied algebra

and electives

Remember me

cool!!!

Karim Mansour

actually electives will be super easy

Remember me

electives include?

Karim Mansour

I have monday Wednesday and friday off

introduction to economics

lol

Remember me

05:18

Jeez...

Karim Mansour

and anthropology

and english

yeah I have been taking 5 hard classes forever

its nice to have 1 semester where its like not too much pressure

Remember me

wha?? anthropology?? Do you guys even get these kind of subjects?

Karim Mansour

to graduate

user147690

@Rememberme Elective options usually are out of 50 things

Karim Mansour

I already took 2

you must take 4 arts electives

like I don't know why I do I even have to take art electives

its stupid

user147690

05:21

@Rememberme You can take the most obscure things

Karim Mansour

@AlexClark here we are required to take 4 art electives

Remember me

As much as I know we don't even name arts in our math courses here

user147690

That sucks, we don't have to do any electives or anything

user147690

@Rememberme I don't know what that means haha

Karim Mansour

I would gladly you know take hard math courses than taking art electives

it sucks

but whatever I will just get easy grade and to hell with it

Remember me

05:23

Did you guys have a course in higher logic?

user147690

Most people say these easy electives will give them good grades, and then end up having so much trouble motivating themselves to do the work they get worse than normal grades, atleast from my friend group

Karim Mansour

yeah but it is a science thing

I guess they consider it it here to not to be art

yeah that is exactly it @AlexClark

actually the two arts electives lowered my average

that I took

Remember me

If I have to chose an elective I will choose psychology if it is there

user147690

Yeah I would only take physics courses as electives or maybe bio or chem as long as they have no practical experiment sessions

Remember me

@AlexC Hows math going?

user147690

05:27

@Rememberme Doing some boring Cardano method stuff :'(

user147690

@Rememberme Finding roots of cubic polynomials the super boring way

Karim Mansour

yeah I did that for my science electives @AlexClark

I took chem,computer science,and alot of physics

Remember me

I wanted to ask you this... Do you have any real analysis problem sheets with you?@AlexC

user147690

@Rememberme From 1.5 years ago yes

Remember me

Can you email them to me?

user147690

05:29

@Rememberme Sure

Remember me

If you have topology can you send them also. I am in real need of loads of questions@ALexC

user147690

Got no topology questions really, unless you include functional analysis I

Remember me

No not functional analysis. I don't know much except measure theory

user147690

You know some measure theory?

user147690

Well the functional analysis 1 was mostly point set topology

Remember me

05:32

@AlexClark Yup some thanks to rudin

leave that then.

user147690

Like product topology and homeomorphisms and such

user147690

Hausodorff spaces etc

Remember me

I might be disturbing you right now , sorry@AlexC But a bit of abstract algebra till rings will be good

user147690

@Rememberme Remind me tonight I guess

Remember me

when precisely?

Time zones... :( that is why

user147690

05:35

Oh my bad different timezones, I should be good to do it in 5 hours or something

user147690

I'm 4.5 hours ahead of you pretty sure, its 3:35pm right now

Remember me

@AlexClark Oh okay, thanks ! Do you know my email?

user147690

@Rememberme Nope

Soham Chowdhury

08:59

@Ted, when you come back: do you know of any other books/sets of course notes besides yours (real expensive here) or Hubbard & Hubbard (apparently you recommend against it) that are nice for multivariable?

I'd greatly prefer one that does differential forms / manifold-y things and such. Yours is basically perfect, from what Balarka says, but, you know, I probably can't justify the price to my parents.

Even pdf course notes are fine.

user174558

09:33

@SohamChowdhury You may want to look at Zorich's Mathematical Analysis I and II.

user147690

@Jasper I personally hate Zorich's mathematical analysis I

user174558

Hello @AlexClark. Why hate it?

user147690

@Jasper I tried it, and after 80 pages I hated it

user174558

What's wrong with it?

user174558

I have been having strange physical symptoms. When I am sleeping my head sometimes jerks violently.

user147690

09:35

@Jasper I can't remember, I think it was a section where it essentially rambled for 20 pages

user174558

There is a new edition coming out next year, with added appendices. I might want to get it.

user174558

It's not epilepsy, but feels quite similar.

user174558

Your blue is as beautiful as mine.

user147690

Sorry was briefly afk. I think this is my favourite identicon(I did try 30 or so, before stopping here)

user174558

30 or so? You are nuts, like me.

user174558

09:44

I think I will retire from the main sites and just come to chat. I think I will keep this account for life.

user174558

@AlexClark After studying Mathematical Logic and Set Theory by O'Leary, I will study Combinatorics and Graph Theory by Harris. These will be my first two books for next year.

user147690

Start studying some commutative algebra with me @Jasper?

Soham Chowdhury

10:39

@Jasper uh, I don't really want an analysis book.

I want a pretty book with a lot of pictures in it. :P

Soham Chowdhury

11:16

what did I miss?

Balarka Sen

you don't want to know, @Soham?

Remember me

Some stuff about people doing sock puppetry @Soham

Soham Chowdhury

oh, screw it then.

user147690

@SohamChowdhury Boring drama

Soham Chowdhury

I thought it was over a long time ago.

user147690

11:18

@SohamChowdhury Nah, always more

Soham Chowdhury

I came back and saw Alec's (removed)s

Balarka Sen

it's never over.

Soham Chowdhury

and got curious

user147690

One of the long term trolls got banned

Soham Chowdhury

ah, good then.

user147690

11:18

Oh I didn't mean that (alecs removed messages). I meant Twink/anti-g**/user

Remember me

Who is the long term troll ?

user147690

What are you working on @SohamChowdhury?

Balarka Sen

@AlecTeal I have half-proved the theorem you wanted to know the proof of. Do you want to know the progress, or do you want me to ping it to you after I have figured it out?

Alec Teal

Hit me.

Soham Chowdhury

@AlexClark Bilinear forms

user147690

11:20

@SohamChowdhury Ahh that's right, from Artin

Remember me

Cool stuff those.. Doing from artin I suppose@Soham?

user147690

@SohamChowdhury Time to learn some Lie algebra then I guess :P

Soham Chowdhury

I did a bit from Artin and am now reading them from KCd's notes.

Yeah, pretty excited about getting to all that stuff.

Remember me

I did from HK

user147690

@Rememberme HK?

Soham Chowdhury

11:20

Hoffman-Kunze

What are you upto, @Rem?

user147690

Don't remember it hmm

Remember me

That's right

Altop, Complex analysis and algebra@Soham

user147690

@Rememberme Did you understand why $[\Bbb Q(\sqrt{2}):\Bbb Q]=2$?

Soham Chowdhury

whew, that's a ton of stuff. from where?

Remember me

Altop, Complex analysis and algebra@Soham

Soham Chowdhury

11:22

@Alex high pitched voice me! me! me!

@Rememberme where are you studying from?

and what are you doing at the moment?

Remember me

Nope . I have too many things at the moment

Munkres, tw gamelin, DF

Respectively

Soham Chowdhury

where are you in each?

user147690

@SohamChowdhury Go for it then :D

Soham Chowdhury

@AlexClark I meant the Q(\sqrt 2) thing

Remember me

Currently altop

user147690

11:24

@SohamChowdhury Yeah, why is the degree $2$?

Balarka Sen

@AlecTeal $f : M \to N$ be a continuous bijection. If $\dim M = \dim N$ : $f$ must be chartwise one-to-one because $f$ is one-to-one itself. By invariance of domain $f$ is open. Open bijective continuous map is a homeomorphism, so you're done. For $\dim M > \dim N$, similar logic : $f$ must be one-to-one chartwise.
So all you have to do is to prove that there is no injective continuous map $\Bbb R^m \to \Bbb R^n$ for $m > n$. Assume there is. Then look at the image of the $(n-1)$-sphere in $\Bbb R^m$ and apply Jordan's theorem. The image disconnects $\Bbb R^n$ (note that the connected compo…

Mike hinted at using Baire category for $\dim M < \dim N$, but I have not thought about it yet.

Soham Chowdhury

@AlexClark as vector spaces, (1,\sqrt 2) is a basis. that's the defn. of degree, right?

user147690

@SohamChowdhury Correct

user147690

Well more specifically it's a two dimensional $\Bbb Q$-vectorspace(with basis $\{1,\sqrt2\}$)

Remember me

@soham in munkres deformation retracts, just started holomorphic functions, finishing sylow stuff(I am going particularly slow there)

Soham Chowdhury

11:26

I use ordered tuples because I'm a cool guy

user147690

@SohamChowdhury :D you are

Soham Chowdhury

well, you have a lot on your plate, @Rem.

user147690

@Rememberme Why is there no simple group of order $150$?

Soham Chowdhury

@Alex is getting all Balarka-y with his questions

user147690

@SohamChowdhury I have waited long enough :P

user147690

11:27

It's been my dream

Soham Chowdhury

I guess something to do with prime factorizations or something? I skipped chapter 7 of Artin :(

Remember me

@AlexC that us why I said . I am slow there. I have to do it again. I left sylow theory in middle(towards the end) so cant answer your question

user147690

@SohamChowdhury Sylow theory, which he said he was finishing

Soham Chowdhury

mmm.

the plot thickens

user174558

@SohamChowdhury Nice pic.

Balarka Sen

11:28

What are you guys discussing about?

Remember me

But currently working on a balarka question. I really need his help on it. @Balarka

Tobias Kildetoft

@AlexClark Because the order is not divisible by $4$ of course :)

user147690

@BalarkaSen I'm giving then questions :D

Balarka Sen

It's getting kind of weird because I'm ignoring Sayan. Maybe I'll unignore him after all.

user147690

@BalarkaSen What why? Oh. I thought you said Soham and was like WTF

Remember me

11:29

Pls help me with the center of the fundamental group question @BalarkaSen

Ya!!!!!

user174558

I see the user and Twink chat accounts have been suspended.

Soham Chowdhury

because he's doing too much stuff and messing it up in the process, like I used to do?

Remember me

Thanks for the Diwali gift @Balarka :P

Balarka Sen

@Soham No, because he googles every single question I give him and claims he cooked it up himself.

Soham Chowdhury

@Balarka, @Alex if $R_B : v \to B(-, v)$:

Remember me

11:30

Reasons @Soham explain you in an email

user174558

@BalarkaSen must be up to no good with that gift.

Soham Chowdhury

how do I do the line for partial application in LaTeX?

user147690

What sort of line is it?

Remember me

Not every one :P

user147690

$B(-,-)$

Balarka Sen

11:31

@Soham $B(-, v)$

Remember me

Okay, now formally. Sorry @Balarka

Soham Chowdhury

ugh

user147690

@BalarkaSen Wink to you too

Soham Chowdhury

never knew that works.

anyway, look at this:

Huy

@Soham long time no see

Soham Chowdhury

11:32

@Huy aye, indeed.

Remember me

I remember @Soham once said Bilinear forma looked liked smilies

Paradox 101

@BalarkaSen if we have limsup of $\frac{x+a}{x+b} sin^2(\frac{1}{x})$ where a and b are real numbers$ then should I first find the sup of the fraction and sin part?

user174558

It is Diwali here too. I was reading how Hinduism is not really a religion but a collection of practices.

Soham Chowdhury

why would $L_B$ (defined in the obvious way) not work?
would that give the transpose, like I think?

Balarka Sen

@Paradox101 I don't want to think about real analysis, Paradox. Why don't you ask Daniel Fischer?

Remember me

11:33

Nicely said @Jasper

Balarka Sen

@Remember Remind me what the center problem was.

Paradox 101

@BalarkaSen ok

user147690

@SohamChowdhury What page is this? I am not familiar with any of it(atleast in this form)

Paradox 101

@Huy can you let me know that if we have limsup of $\frac{x+a}{x+b} sin^2(\frac{1}{x})$ where a and b are real numbers$ then should I first find the sup of the fraction and sin part?

user174558

@AlexClark I think atleast should be at least.

Balarka Sen

11:34

Something self-homotopy equivlence, something something image of $\{x_0\} \times I$ being in the center.

Soham Chowdhury

Jasper speaks the truth.

user174558

Buddha speaks the truth.

Soham Chowdhury

@Jasper technically true, but the majority of Hindus believe a lot of very similar things. i.e. it's more uniform, in practice, than what that statement would have one believe

Remember me

I have to run now. Sorry @Balarka leaving the question. I am also on my phone so I will come with the whole question on altop chat

Soham Chowdhury

@AlexClark this isn't Artin.

Balarka Sen

11:35

ok.

Soham Chowdhury

Balarka, any help?

Balarka Sen

what's the question?

Soham Chowdhury

saw the screenshot?

Balarka Sen

Yes.

user174558

@SohamChowdhury I currently do not subscribe to any religion except Theravada Buddhism.

Soham Chowdhury

11:36

I'm checking if using $L_B$ instead of $R_B$ would give the transpose of the correct matrix.

Balarka Sen

You're losing me with notations. What's $L_B$?

Soham Chowdhury

@Jasper that's nice, but where does that follow from?

arrey it's like Hom functors

$L_B: v\mapsto B(v,-)$

$R_B:v\mapsto B(-,v)$

Balarka Sen

OK. So you're checking if the matrices for these two are transposes of each other?

Soham Chowdhury

yes.

user174558

@SohamChowdhury Nowhere.

Soham Chowdhury

11:38

of course, respective to a given basis of $V$ and its corresponding dual basis for $V^{\wedge}$

Agawa001

i was banned in another room for speaking religious stuff and now they are discussing it openly, dont really know how people's mind work, i just avoid to get stuck in a clash of cultures henceforth.

Balarka Sen

Gotcha. So is that the question?

Soham Chowdhury

that is my question, yes.

why would not $L_B$ work?

my answer is that it would give the transposed matrix.

Balarka Sen

Are you sure it'd give me the transpose? Because I haven't checked.

Soham Chowdhury

because $L_B(e_j)(e_i) = B(e_j,e_i)$ whereas $R_B(e_j)(e_i) = B(e_i,e_j)$

looks like transpose to me.

I actually came up with the answer just after asking you guys. this happens too much :P

Balarka Sen

11:41

That seems fair.

I agree with you.

I mean, of course - since $L_B(v)(w) = B(v, w)$ and $R_B(w)(v) = B(w, v)$, these two maps are transpose of each other, hence so are the matrices :P

I wasn't paying attention.

Soham Chowdhury

once you parse all the notation, it's essentially obvious.

Balarka Sen

mhm.

oh, by the way, have you read the proof of Cayley-Hamilton theorem from Artin? That's something which comes up in module theory/commutative algebra in a much more enhanced and powerful form - namely, Nakayama's lemma.

Soham Chowdhury

the proof felt like cheating, actually :P

"we won't have distinct eigenvalues (generally), but we can get a convergent sequence all of whose elements do"

Balarka Sen

it's a beautiful proof.

Tobias Kildetoft

@SohamChowdhury Does that work in the usual topology, or does he use the Zariski topology?

Balarka Sen

11:49

@TobiasKildetoft Artin proves it over $\Bbb R$.

Soham Chowdhury

no, the best proof is "subsitute $t=A$ into the expression $\det (tI-A)$, haha
(I know that doesn't work)

Tobias Kildetoft

@BalarkaSen Ahh. Same proof works over any field (or even integral domain, not sure if it can be extended to all rings)

Balarka Sen

@TobiasKildetoft Really? How so?

Tobias Kildetoft

@BalarkaSen Embed into an algebraically closed field to reduce to the case of such

the note that the set of matrices with distinct eigenvalues is open in the Zariski topology and hence dense

Balarka Sen

oh wow

Tobias Kildetoft

11:52

(it is given by the non-vanishing of the discriminant of $det(A - \lambda I)$)

and since the statement is easy to show for these matrices (being diagonalizable), it follows

Soham Chowdhury

that is very slick.

Tobias Kildetoft

(using that affine varieties are separable, so if a morphism is $0$ on a dense set, it is $0$ everywhere)

Soham Chowdhury

correct me if i I'm wrong.

this hinges on the fact that for (2), diagonal entries have to be zero unless your field has characteristic 2.

Balarka Sen

yes

skew-symmetric matrices have diagonal entries = 0 : you need to have $a + a = 0$, clearly impossible for nonzero $a$ if you're not in char 2 field.

cp101020304

Just a really simple question

Soham Chowdhury

11:57

that's what I thought.

cp101020304

is the function f(n) = n^3 surjective over the domain of all integers?

i.e $\mathbb{Z}$

Tobias Kildetoft

@cp101020304 with what codomain?

Balarka Sen

f is a function from integers to integers? then no.

2 is not a cube of any integer.

cp101020304

from Z->Z sorry i should have specified

@BalarkaSen thank you sir

Soham Chowdhury

ei, @Balarka.

Paradox 101

12:02

How do I prove that a function is uniformly continuous if the function in question is written in terms of the integral of another function which is riemann integrable?

Balarka Sen

mhm?

Soham Chowdhury

does the space of all (nondegenerate) bilinear forms on $V$ have any structure?

subgroup of $GL_n$?

i.e. $GL_n/(A\sim B$ if $P^tAP = B$ for some $P)$

is that a group?

Balarka Sen

@SohamChowdhury to each billinear form $V \times V \to k$, you can associate a linear map $V \otimes V \to k$.

Soham Chowdhury

ohhh

$\text{Hom}(V\otimes V,k)$?

Balarka Sen

\otimes.

yes.

so symmetric 2-forms on $V$ ;)

Soham Chowdhury

12:08

2-forms as in . . . differential forms?

and why symmetric?

Balarka Sen

yes. but these are symmetric.

wedge is antisymmetric.

$a \otimes b = b \otimes a$, but $a \wedge b = - b\wedge a$

Tobias Kildetoft

@BalarkaSen $\otimes$ is not symmetric

Soham Chowdhury

I thought you couldn't do that

a \otimes b is just that. you can't flip them.

(AFAIK, of course)

Balarka Sen

my internet is horrendous, sorry

@TobiasKildetoft yikes! I was thinking of symmetric tensors. of course not.

ok, better name?

Tobias Kildetoft

Not sure I have seen a notation for elements of a symmetric power

Balarka Sen

12:15

unsymmetrized forms, maybe?

meh, who cares. it's just $\hat{V} \otimes \hat{V}$.

Huy

@Paradox101: But the limsup of the fraction is $\infty$

Balarka Sen

darn this internet connection.

@SohamChowdhury Yes, you are right, I am being silly. Confusing with symmetrized tensor products, where $M \otimes N$ is defined by qt. of the free module on $M \times N$ by the usual billinear relations + $a \otimes b - b \otimes a = 0$

Of course, in general, tensor products need not satisfy that last thing.

Paradox 101

@Huy yes but if I rewrite the fraction in terms of two fractions which are being added and multiply them with the sin part won't that make things easier?

Huy

@Paradox101: can you specify what you exactly want to do?

Paradox 101

Also can you explain that given a function how do I prove that it's uniformly continuous if the function in question is written in terms of the integral of another function which is riemann integrable? I tried writing it in terms of |g(t)-g(s)|< $\epsilon$ but then that reduces to epsilon is greater than zero

Is this correct @Huy ?

Huy

12:48

@Paradox101: sorry, but "limsup" can be anything. you need to specify what lim sup

Paradox 101

That isn't specified in the question @Huy

Huy

then it's not a well defined question

I can't expect my students to find $\lim \frac{1}{n}$

Paradox 101

All that's meniond is that a and b are real numbers

Huy

that question doesn't make any sense

Paradox 101

yes

but if for instance i was x approaches infinity what would it be? For x approaches ?@Huy

Huy

12:51

$0$ I think, but I might be wrong

Paradox 101

@Huy how will you get $0$?

Huy

the sin part is 0 and the other part is a constant

Paradox 101

I mean if we just take the sup of the function then it should be 1 no?

0celo7

the sin part

no sinning pls

skill patrol

says who?

0celo7

12:59

Me

A cat

A well-behaved cat

Huy

but as $x \to \infty$, $\sin(1/x)$ doesn't oscillate anymore

it just gets smaller

0celo7

@Huy small but mighty

Paradox 101

@Huy ok but then what function does sup serve?

Huy

if you take $\limsup_{x \to \infty} \sin(x)$, then you get $1$

even though $\lim_{x \to \infty} \sin x$ doesn't exist

Soham Chowdhury

@BalarkaSen reading "free module" as "vector space", that agrees with what I know

skill patrol

13:02

:O

welcome back @SohamChowdhury

Soham Chowdhury

I took a break.

skill patrol

icic

Soham Chowdhury

actually no more math tonight, probably. I have to study physics.

skill patrol

that can be the same thing :P

Paradox 101

@Huy but in this context if we take only the sup of the function what should be the right answer?

Huy

13:07

What sup

you need to specify

skill patrol

@0celo7 that would make you a cool cat

Paradox 101

@Huy but don't we need to specify what x approaches to for the limit? Shouldn't we be able to simply take the supremum of the function?

Chris's sis the artist

Say $m$ is a positive even integer. Then find $$m+\frac{1-m^2}{3!}+\frac{(3-m^2)(1-m^2)}{5!}+\frac{(5-m^2)(3-m^2)(1-m^2)}{7!}+‌\cdots $$

Huy

@Paradox101: if you take the sup of a function $f(x)$ you need to specify what $x$-values exactly we are allowed to use

it doesn't make sense to write $\sup f(x)$

only something like $\sup_{x \in D} f(x)$ where $D \subseteq \mathbb{R}$ makes sense

Chris's sis the artist

@robjohn @r9m see the one above, it's fun. :-)

Paradox 101

13:12

@Huy ok. So then in this case if x tends to $0$ the limsup won't exist?

Huy

why not?

Paradox 101

@Huy because sin^2 of infinity isn't defined?

Huy

$\lim_{x \to \infty} f(x)$ doesn't mean "we plug in $\infty$ for $x$"

I just told you before that $\limsup_{x \to \infty} \sin(x) = 1$

Paradox 101

@Huy but in this case it's $\limsup_{x \to \0} \sin(\frac{1}{x}) = 1$

Huy

so?

Paradox 101

13:17

So then as x tends to zero, x inverse tends to infinity

Huy

$1$ isn't quite "doesn't exist"

Paradox 101

yes sorry i forgot to erase that

Chris's sis the artist

$$\lim_{m\to2}\left(m+\frac{1-m^2}{3\cdot 3!}+\frac{(3-m^2)(1-m^2)}{5\cdot 5!}+\frac{(5-m^2)(3-m^2)(1-m^2)}{7\cdot 7!}+‌\cdots\right)=\frac{\pi}{2}$$

robjohn

@Chris'ssistheartist do we need the limit?

Chris's sis the artist

@robjohn No, just a way of posing things is a nicer way.

Paradox 101

13:34

If we are given the above function, how do I prove that g is differentiable? Can I state that by using FTC 1 we can say that g is an antiderivative of f?

Huy

$g(x) = |x|$ is the antiderivative of $f(x) = \operatorname{sgn}(x)$ but $g(x)$ is not differentiable

Paradox 101

@Huy then how do we show that it is differentiable? We don't know whether f is continuous

Paradox 101

13:56

In this case the derivative of g(x)= F'(x+c)-F'(x-c)?

Huy

14:08

if you don't know that $f$ is continuous, then that function isn't necessarily differentiable, as my example shows

Paradox 101

so then do we use mean value theorem? @Huy

So i can say that g(x)=F(x+c)-F(x-c)

Huy

???

Paradox 101

@Huy i'm just trying to prove that g is differentiable.since I can't figure it out using FTC I thought to maybe manipulate mean value theorem?

Huy

but $g$ isn't differentiable if you don't at least assume $f$ to be continuous

Paradox 101

so then assunming that f is continuous is the only way to prove the differentiability of g?

r9m

14:36

@Chris'ssistheartist I don't know .. tried it for a while though (can't see anything) .. :) However you might like $\displaystyle m+\frac{1-m^2}{3!!}+\frac{(3-m^2)(1-m^2)}{5!!}+\frac{(5-m^2)(3-m^2)(1-m^2)}{7!!}‌+‌\cdots $ .. turned out to be interesting when I was trying to deal with your sum :)

MickLH

I was trying to turn it into a hypergeometric series but I think I'm too tired to see it, I got stuck here: $$m+{{\Gamma\left(-{{m^2}\over{2}}\right)\,\sum_{n=0
}^{\infty }{{{\left(1+2\,n-m^2\right)\,\Gamma\left(2\,n-m^2\right)
}\over{2^{n}\,\Gamma\left(n-{{m^2}\over{2}}\right)\,\Gamma\left(4+2
\,n\right)}}}}\over{\Gamma\left(-m^2\right)}}$$

r9m

Holy cow! .. turning it Hypergeometric is the last thing I wanna try! (I'm severely allergic to that thing ,, )

r9m

14:56

BBL

Chris's sis the artist

@r9m Back.

r9m

@Chris'ssistheartist hey (I was about to leave for dinner .. ) :) maybe give me some hint to think about while I crunch my fries (over dinner) :-)

Chris's sis the artist

@r9m Hey! I'm in trouble with installing a latex file, d*mn. I do all perfectly.

@MickLH Nice that thing! :-)

@r9m It has a nice form?

r9m

@Chris'ssistheartist ya! That thing telescopes :D (found it while I was trying to make your series telescope into something)

Chris's sis the artist

@r9m ups :-)

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$Mathematics$ Mathematics