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May
14
comment Dirichlet problem in the disk: behavior of conjugate function, and the effect of discontinuities
@Yes You exhibit nice answer. I can understand your (counter)example intuitively but cannot write mathematically rigid for example with your 1st example for $F$, such as how the boundary arcs are maped by your conformal map $F$, where the imaginary part of $F$ goeswhen $z$ tends to other point except the two points on the boundary of the unit disk which are sent into infinity by $F$? Can you explain a little?
May
13
revised Should a certain entire function be a polynomial?
edited tags
May
13
answered Is the set of $f\colon U \to \mathbb C$ with $f(z_0) = -1$ and $f(U) \cap \mathbb Q_{\geq 0} = \emptyset$ a normal family?
May
13
revised Should a certain entire function be a polynomial?
added 92 characters in body
May
13
revised Should a certain entire function be a polynomial?
added 416 characters in body
May
13
comment An entire function with an integral bound for $f'/f$ on a sequence of circles must be a polynomial
This question is already answered here
May
13
revised Should a certain entire function be a polynomial?
added 280 characters in body
May
13
comment Should a certain entire function be a polynomial?
@Will Jagy For the motivation of my question, see this math.stackexchange.com/questions/498945/….
May
13
asked Should a certain entire function be a polynomial?
May
8
comment Find a certain analytic function
@ajd This is really a wonderful answer!
Feb
10
accepted Monic and epic implies isomorphism in an abelian category?
Feb
4
accepted On compact, simply connected Lie group and its subgroup
Jan
26
awarded  Taxonomist
Jan
12
comment Evaluating $\int^{\infty}_{0}{\frac{\ln x}{(1+x^2)^2}dx}$
This wiki example also deals with this integral using contour integration and residue theorem:en.wikipedia.org/wiki/…
Jan
12
comment contour integration: $\int_{-\infty}^{\infty} \frac{\cos x + x \sin x}{1+x^2} dx$
Just a caution: Since a priori we don't know whether this integral, we indeed need to choose a slight different contour, a rectangle on the upper half plane, for details, see P 156, 3) in the book "complex analysis" by Ahlfors, which deals with the case with simple zero at infinity.
Jan
12
revised Evaluating $ \int^{\infty}_{-\infty}\sin\left({\pi}^{4}x^{2}+\frac{1}{x^2}\right) dx$
Just a minor typo!
Jan
12
suggested approved edit on Evaluating $ \int^{\infty}_{-\infty}\sin\left({\pi}^{4}x^{2}+\frac{1}{x^2}\right) dx$
Jan
12
comment Calculating $\int_{0}^{\infty}\sin(x^{2})dx$
Sorry, not a constant, but still a integrable function on the closed interval.
Jan
12
awarded  Critic
Jan
12
comment Calculating $\int_{0}^{\infty}\sin(x^{2})dx$
I think the best way to obtain what you want is to use the Lebesgue dominated theorem: as R tends to infinity, the integrand tends to 0 and is less than a constant which is integrable on a finite interval.