21,783 reputation
31951
bio website maths.lth.se/matematiklth/…
location Lund, Sweden
age 42
visits member for 3 years, 2 months
seen 1 hour ago

Associate professor, Lund University. Research interests: several complex variables, in particular pluripotential theory.


11h
revised Find all holomorphic functions $f:\mathbb{C}\setminus\{0\}\rightarrow \mathbb{C}$
added 160 characters in body
1d
comment Find all holomorphic functions $f:\mathbb{C}\setminus\{0\}\rightarrow \mathbb{C}$
@DanielFischer You're right of course.
1d
revised Find all holomorphic functions $f:\mathbb{C}\setminus\{0\}\rightarrow \mathbb{C}$
added 43 characters in body
1d
answered Find all holomorphic functions $f:\mathbb{C}\setminus\{0\}\rightarrow \mathbb{C}$
2d
comment General Formula for Principle Square Root of Complex Number
You should probably explain why $\sqrt{\cos^2 (\theta/2)} = \cos(\theta/2)$ (and not $-\cos(\theta/2)$). In other words, since we are looking for the principal square root, we choose $\theta \in (-\pi,\pi)$.
2d
comment General Formula for Principle Square Root of Complex Number
This only shows that the expression is a square root, not necessarily the principal square root.
Jan
27
comment Why $\zeta(-1)=-1/12$? Doesn't defining it like this instead create problems?
$\zeta$ is not defined via the series when $\operatorname{Re} s \le 1$, but via analytic continuation
Jan
27
revised Tossing two dice with sum equal to 4?
deleted 20 characters in body; edited title
Jan
27
comment Imaginary part of $ln(\sqrt{i})?$
Absolutely, but casual reading of the answer might be misleading.
Jan
27
comment Imaginary part of $ln(\sqrt{i})?$
I'm assuming that you are hinting at $(e^{i\pi})^{1/4}$. Note that $(z^a)^b = z^{ab}$ is false in general for complex numbers. (Or even for non-positive real numbers.)
Jan
27
comment Imaginary part of $ln(\sqrt{i})?$
Your equality $\log \sqrt z = \frac12 \log z$ only holds for certain choices of branches of the complex $\sqrt{}$ and $\log$ functions.
Jan
26
revised Let g and h be any functions from naturals to (0,infinity)
Fixed tags and formulas
Jan
26
reviewed Leave Open Rank in row echelon form
Jan
26
reviewed Leave Open $P(x)=x^3+ax^2+bx+c$, Proof $e^{P(x)}=\sin x$ has a solution.
Jan
26
comment Modulus of a complex expression
@JonasMeyer This is seriously weird. I copied the link from one browser tab to the next: Yet another attempt math.stackexchange.com/questions/191453 Wow. finally.
Jan
26
comment Cauchy integral formula: can it be proved like this?
If you are comfortable with complex differential forms, there is no need to do a detour over $dx$ and $dy$. You can check that $$df = \frac{\partial f}{\partial z} \,dz + \frac{\partial f}{\partial \bar z}\,d\bar z$$ and since $f$ is assumed to be holomorphic, $\frac{\partial f}{\partial \bar z} = 0$.
Jan
26
answered Radius of convergence of $\sum_{n=0}^\infty a_n z^{n^2}$
Jan
25
awarded  Good Answer
Jan
24
comment Analytic bounded in the half right plane is identically zero provided that $\limsup_{x \rightarrow \infty}$ $\frac{\log|f(xe^{ni})|}{x}\leq-n$
Your title and the first sentence contradict the rest of your question. ($e^{-z}$ is bounded on the right half plane.) Please clarify the question a little.
Jan
24
revised Does $\sin(x+iy) = x+iy$ have infinitely many solutions?
Avoid all-math titles