@PeterTamaroff Idk, maybe try to find an integral representation of the polylogarithm and manipulate it so your limit can be evaluated in terms of that
What I like best about this menu, is that it changes automaticly if new content is available. So I only need to add the images, and the rest works automatic :)
when i bought the 7th edition of the translation of schaums in linear algebra , i was so sad ! every page have at least errors , and the style of the text is poor not like the english one . after that , i decided to start learning maths in english !
@skullpatrol one of my teachers sent me an e-mail yesterday and wrote at a certain point: " ... the beauty of the solutions made me cry. So great!" Actually, I sent him $7$ solutions to a calculus question ...
That feedback made me feel just nice.
@skullpatrol hehe, nice picture.
@skullpatrol however, it's better to be in an excellent state of mind no matter the others say, think about you.
by the way in general terms in order for the system to be solvable by Gauss and to produce a proper eigenvector, should the new matrix always have a determinant equal to 0? Because otherwise I can use Cramer and it gets me 0 for x,y and z
@robjohn Do you want me to "roll back"? Fine...but that might appear like I'm trying to "bump the question." (OH NO!) If the point is: do not edit old posts, Fine... I won't. Did this issue come up when Jasper edited all his old posts before leaving?
@amWhy If Jasper did it just before leaving, it did him little good. I think I had told him not to, but I didn't see it.
@amWhy It just caught my attention when I went to answer and I saw that everything was over 6 months old and there was just this minor, and what seemed backward, edit.
The point of Jasper's editing, and the point of my editing, was not to "do (him) me any good." I came across the post when searching for a duplicate...didn't even notice the "date" of the post...Again. Apologies all
I was trying to re-read my post, and I personally find the $\times$ distracting, as to what's happening. I didn't look to see why I chose to use it in the first place. Again. APOLOGIES.
@LittleChild the same thing works for convergent power series, and essentially all complex differentiable functions are locally convergent power series.
@robjohn I've been trying to get mathjax to work on my website, for some reasons my comment system block the mathjax. However if I click on chatjax, it does work. I wonder if it possible to load chatjax automaticly on my website. (Sorry i'm a little bit of a noob with programming )
Someone was wondering about the asymptotics of $\sum_{v=0}^n\binom{n}{v}^k$ for $n\to\infty$ some days ago here. Anyways $$\sum_{v=0}^n{\binom{n}{v}}^k\sim \frac{2^{nk}}{\sqrt k}\left(\frac{2}{n\pi}\right)^{\frac{k-1}2}$$
@Kasper ChatJax is run completely in the browser, but you need a special Javascript header (that is included in the ChatJax bookmark) to make the MathJax render
whats the difference between $\forall x\in \mathbb{Z} \exists y\in \mathbb{Z}\left ( y>x \right )$ and $\exists y\in \mathbb{Z} \forall x\in \mathbb{Z}\left ( y>x \right )$ i see no difference at all.
For example, what is the different between "For each person $P$ in the world, there is a person that loves $P$" and "There exists a person $P$ such that everybody in the world loves"?
@robjohn haha, but I really don't understand how mathjax doesn't work, and chatjax does work, maybe that is beyond my scope :P I always thought of chatjax as mathjax on demand
@Kasper It is, but if you want others to see the content of your pages, you need to have the MathJax headers in the <head> section of your page. Otherwise, you require the reader to install ChatJax
@vvavepacket In the first, we're saying the for every iPad there exists a case, but this last case is a function of the iPad I give you. In the second case, what we interpret is that there is one "universal" case for any iPad you give me. See the difference?
Look at it this way "For every key, there is a door that key opens." and "There is a key that opens every door."
@vvavepacket Hmm, not really, but I did mess up. What you mean is "For every key, there is a door that key opens". and "There is a door that is opened by every key."
@robjohn hm.. but if I put mathjax in the header, only some latex is converted, if I put chatjax in the header, all latex is converted (including the latex in the comment section)
@robjohn Goes as follows: suppose $\varphi:[0,\infty)\to\Bbb R$ is such that, for $x\geqslant M$ we can write $$\varphi(x)=\sum_{k\geqslant 0}a_k x^{-k}$$ Then $\sum\limits_{k\geq 1} \varphi(k)$ converges $\iff a_0=a_1=0$.
What I want to produce is a rigorous proof, as opposed to some handwavy argument using $p$-series.
@robjohn Heh, sure-.
Note that there is no restriction on the $a_k$. Of course, the series converges absolutely on $\{x>M\}$.
So one has to argue for example that $$\sum_{k>M}\sum_{\ell\geq 2} \frac{a_\ell}{k^\ell}=\sum_{\ell\geq 2}a_\ell \sum_{k>M}\frac{1}{k^\ell}$$ and that this last sum converges, @robjohn
I just started studying analysis (about half way through chapter 1 of rudin), so now I am getting into the exercises about complex numbers. I am curious how much complex analysis vs real analysis is in further chapters, or maybe there is a really close correspondence so there isn't even much of a distinction between the real and complex analysis? (I don't know much about analysis so I am not sure how easily real techniques extend to complex techniques)
@Bageer Well, it is good to know about complex numbers. And sometimes we can use some about them to tackle real analysis problems. For example, in the computation of $$\sum_{k=1}^n \sin k$$
Question:
Given $f(z) = 3z^2 + 9z^3 -z$.
1. Find $f\prime(z)$
2. Find $f(z)$ when $z = 3 + 2i$
3. Use Cauchy-Riemann to find if $f(z)$ is differentiable at $3 + 2i$
My Attepmt:
$f\prime(z) = 6z + 27z^2 - 1$
$$f(3 + 2i) = 3(3+2i)^2 + 9(3+2i)^3 - (3 + 2i)$$
$$= 3(9-4+6i)+9(9-8i+54i-...
