Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

learn more… | top users | synonyms (1)

7
votes
2answers
108 views
+250

Construction of a continuous function which maps some point in the interior of an open set to the boundary of the Range

I was studying the Inverse function theorem when I came across the following problems : (Let the closed set $V$ i.e the range have non-empty interior) Does there exist a continuous onto ...
1
vote
1answer
117 views
+50

It is possible to get a closed-form for $\int_0^1\frac{(1-x)^{n+2k-2}}{(1+x)^{2k-1}}dx$?

It is know that $$H_n=-n\int_0^1(1-t)^{n-1}\log (t)dt,$$ see [1], where $H_n=1+1/2+\ldots+1/n$ it the nth harmonic number. Then I believe that can be used for $x>0$ ...
4
votes
2answers
83 views
+100

A sequence of continuous functions which is pointwise convergent to zero and not uniformly convergent on any interval.

The exercise is to construct a sequence of continuous functions $f_n:\mathbb{R}\rightarrow \mathbb{R}, n\in \mathbb{N}$ , which is pointwise convergent to $f(x)=0 , x\in \mathbb{R}$ and not uniformly ...
1
vote
2answers
370 views
+150

Laplacian of a radial function

Let $f:\mathbb{R}^n\to\mathbb{R}$ be a radial function, i.e. $f(x)=f(r)$ with $r:=\left\|x\right\|_2$. As stated at Wikipedia $$\Delta f=\frac{1}{r^{n-1}}\frac{d}{dr}(r^{n-1}f')$$ What's the most ...