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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.
Jan
12
comment Calculating $\int_{0}^{\infty}\sin(x^{2})dx$
Just use your inequality cannot solve the problem!
Jan
8
awarded  Popular Question
Jan
8
revised If an irreducible $f(x)$ divides $f(x^2)$, then its splitting field is $F(\alpha)$ for any root $\alpha$ of $f(x)$?
edited title
Jan
8
asked If an irreducible $f(x)$ divides $f(x^2)$, then its splitting field is $F(\alpha)$ for any root $\alpha$ of $f(x)$?
Jan
8
comment The units of $\mathbb Z[\sqrt{2}]$
How do you get that $1+\sqrt{2}$ is the smallest unit greater than 1?
Dec
31
comment How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
@Jyrki Lahtonen: Yes, that's what I mean (I should have written as you did).
Dec
31
comment How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
This argument also applies to any field of characteritic $p$.
Dec
11
awarded  Caucus
Dec
2
awarded  Excavator
Dec
2
revised measure of the image of the the unit open disc by a holomorphic map
deleted 1 character in body