I'm not sure wether or not the following sum uniformly converge on $\mathbb{R}$ :
$$\sum_{n=1}^{\infty} \frac{\sin(n x) \sin(n^2 x)}{n+x^2}$$
Can someone help me with it? (I can't use Dirichlet' because of the areas where $x$ is close to $0$)
This is a lovely question: prove that removing two squres from an 8x8 chessboard leaves a board that can be partitioned into 1 by 2 rectangles iff the two missing squares have opposite colours
@Pedro: There is a shuttle that runs to Athens, but I'll come get you. If you're really following through on this, send me an email with particulars before we get too far.
Yup. And I almost had a bad accident driving home from Atlanta at night 15 years ago when one tried to jump in front of me on a dark road when I was driving 65 mph.
@Alizter How did you generate your previous images of dyhedral groups ? All i get for D_100 is einsteink.freezoy.com/Results/Gradient.png (it's colored based on the kind of symmetry and its number )
Good way to generate gradients though :c but unexpected
Would I be right in stating that f is continuous at x on a first countable space iif whenever we have a sequence x_n -> x it follows that f(x_n) -> f(x) ?
From calculus 1 we learnt the three conditions for continuity at a point of a real function f:R -> R...the limit exists, f is defined at the point and limit of f is equal to f a t the point...is there additional structure on R^n other than first count-ability which allows for this definition?
I read about the system of $n$ equations in the link below.
I wonder how it behaves for growing $n$. Does it converge ?
http://math.eretrandre.org/tetrationforum/showthread.php?tid=889
Here it is explicit :
Consider the polynomial $f_n(x) = x^n + a_1 x^{(n-1)} + a_2 x^{(n-2)} + ...$
Now solve...
@Ted Okay but I'm just interested as to why the functions f:R -> R has continuity defined in this special way...so I was wondering what additional structure allows for it, since I know it at least has first count-ability...
Im looking for a real-analytic function $f(z)$ such that for any $z$
$1) $$f(z+p) =f(z)$
With $p$ a nonzero real number and where $z$ is close to , or onto the real line such that $z$ is in the domain of analyticity.
$2)$ $f(z)= 0 + a_1 z + a_2 z^2 + a_3 z^3 + ...$ where more than $50$ % of ...
He's saying that the distribution of binomial coefficients (the entries of Pascal's triangle for large $n$) look a lot like the normal distribution, the Gaussian. @Hippa
Yes, @Moses, every metric space is first-countable.
Reminds me of using vacuum flasks back in the day @Studentmath. Hydrocarbons with fairly low vapor pressure while under vacuum would boil rather violently, yet the outside of the flask would be ice cold.
I'm not sure wether or not the following sum uniformly converge on $\mathbb{R}$ :
$$\sum_{n=1}^{\infty} \frac{\sin(n x) \sin(n^2 x)}{n+x^2}$$
Can someone help me with it? (I can't use Dirichlet' because of the areas where $x$ is close to $0$)
I read about the system of $n$ equations in the link below.
I wonder how it behaves for growing $n$. Does it converge ?
http://math.eretrandre.org/tetrationforum/showthread.php?tid=889
Here it is explicit :
Consider the polynomial $f_n(x) = x^n + a_1 x^{(n-1)} + a_2 x^{(n-2)} + ...$
Now solve...
