Lao-tzu
Reputation
651
Next privilege 1,000 Rep.
Create tags
 Feb10 accepted Monic and epic implies isomorphism in an abelian category? Feb4 accepted On compact, simply connected Lie group and its subgroup Jan26 awarded Taxonomist Jan12 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/… Jan12 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. Jan12 revised Evaluating $\int^{\infty}_{-\infty}\sin\left({\pi}^{4}x^{2}+\frac{1}{x^2}\right) dx$ Just a minor typo! Jan12 suggested approved edit on Evaluating $\int^{\infty}_{-\infty}\sin\left({\pi}^{4}x^{2}+\frac{1}{x^2}\right) dx$ Jan12 comment Calculating $\int_{0}^{\infty}\sin(x^{2})dx$ Sorry, not a constant, but still a integrable function on the closed interval. Jan12 awarded Critic Jan12 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. Jan12 comment Calculating $\int_{0}^{\infty}\sin(x^{2})dx$ Just use your inequality cannot solve the problem! Jan8 awarded Popular Question Jan8 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 Jan8 asked If an irreducible $f(x)$ divides $f(x^2)$, then its splitting field is $F(\alpha)$ for any root $\alpha$ of $f(x)$? Jan8 comment The units of $\mathbb Z[\sqrt{2}]$ How do you get that $1+\sqrt{2}$ is the smallest unit greater than 1? Dec31 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). Dec31 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 $p$. Dec11 awarded Caucus Dec2 awarded Excavator Dec2 revised measure of the image of the the unit open disc by a holomorphic map deleted 1 character in body