I find no good reason to believe that. Even if I'd believe that, it wouldn't change my opinion that you are a mathematician, as well as an expert in the field of closed forms of I&S
@robjohn I like hypergeometric functions much more than other real analytic function. Even more than Lerch's zeta.
Exercise : Reduce the quartic curve $y^2 = x^4 + 1$ to a cubic form by a $\Bbb C$-rational transformation.
@GabrielR. A topological anti-Riemann, super-Desaregous, ultra spaced, hyperelliptic super-genus example of a A-hypergeometric, semimodular, pseduosemistable Riemann surface.
@robjohn Although I have some solutions at hand, I wonder why the way you used yesterday is more powerful than all mines.
@robjohn $\displaystyle \sum_{k=1}^{\infty} \left(\frac1k-\frac1{k+n}\right)$. This makes the difference. Actually, it makes $n$ from denominator disappear.
I need more detailed help than what I'm getting in the answer to my question.
It's driving me batty, because I want to learn so badly, and I've been trying and trying to apply the hint the guy who answered me gave me, it's still not working out, and he doesn't seem to respond to follow ups.
I am having difficulty with the following proof:
Generalize the weak lower semi-continuity of$L^{p}$ norms to all $1\leq p < \infty$; i.e., show that if $u_{n}\to u$ weakly in $L^{p}$, then
$||u||_{L^{p}}\leq \inf_{k}||u_{k}||_{L^{p}}$.
We were given the following hint: Consider the integral $...
@N3buchadnezzar I think that they wrote $h$ wrong... It should be $h(\theta)=\cos(\theta)e^{\cos(\theta)}\cos(\sin(\theta)) - \sin(\theta)e^{\cos(\theta)}\sin(\sin(\theta))$
@N3buchadnezzar These problems are usually integrating the real part of an analytic function around the unit circle, but the $h$ they give is not the real part of the analytic function they've given above.
@Julien I am really unsure, my obvious answer would be when cos(x) is irrational or sin(x) irrational, or when both are irrational and when you divide them you get another irrational.
@KarlKronenfeld yeah, had to find a specific subgroup of the positive Q's (speaking of irrationality) that is of the ordinal w^2, so I think w^a where a is a natural number is almost certain, question can we get that a to w..
In fact I am working on my exercise, and I would like to know if I can put an infinite number of points on the unit circle which has an irrational distance between all of them
No, because I assume things must have to cancel in order to get just $||u||_{L^{p}}\leq \inf_{k}||u_{k}||_{L^{ p}}$, otherwise, why bother introducing all that v stuff in the first place? So, no, there is algebra I'm having trouble with, I suppose.
Everybody knows how you can tell if an elephant's been in your fridge -- footprints in the butter. But how can you tell if the elephant has been trying to follow Szemeredi's original proof of his theorem on original progressions?
@TedShifrin Because for a finite number of points on the unit circle which has an rational distance between all of them and the proof using the fact that if $\tan\theta$ is rational then this one $\sin \theta$ is that too.
@Studentmath Its credibility is in question, since I have no idea who made that claim. Anyway Joel David Hampkins reiterates that claim in this answer: math.stackexchange.com/a/37161/67848
@Ted, Davide followed up. He said I should apply the definition of weak convergence right after my first $\leq$, which he says should be an inequality, and that should do the job. Maybe I'm unclear about the definition of weak convergence?
@Ted Well, I meant to refer to my difficulties in following Szemeredi's proof but it might be a bit of a longshot that anyone here is available to help me with that. @Mike, I'm referring to you here??!!
@Ted, I can leave your name out of it if you request that. But an expert would only be useful to me if they are really available. Getting no reply or getting a reply that says "Can't help, I'm busy." won't be so useful to me.
@TedShifrin My claim about $\omega^2$ being the upper limit yesterday was shil bult in its prime form. (1) I found a way to embed things like $\omega^n$ for all $n$, and (2) then it turns out any countable linear order embeds $\mathbb Q$. :)
If $\tan\theta$ is irrational then $\sin(2\theta)$ is irrational because we have : $\sin(2\theta)=\frac{2tan(\theta)}{1+tan^2(\theta)}$. It is correct ?
@Paul: Neil Lyall, Akos Magyar (who's currently at UBC but returning to UGA), and Alex Rice (about to take a postdoc at Rochester but currently at Bucknell).
@Ted Stack overflow is also a possibility but there's a $1000 fine for not tex formatting the questions correctly, and I'm not the world's greatest expert in that domain.
How though??? That's the part I'm having the most trouble with us keeping those q norms and p Norns in there. There must be a trick to it, but nobody will tell me what it is!!
I am having difficulty with the following proof:
Generalize the weak lower semi-continuity of$L^{p}$ norms to all $1\leq p < \infty$; i.e., show that if $u_{n}\to u$ weakly in $L^{p}$, then
$||u||_{L^{p}}\leq \inf_{k}||u_{k}||_{L^{p}}$.
We were given the following hint: Consider the integral $...
