# Julián Aguirre

Bilbao, Spain

Age: 59

 4h comment Evaluating real improper integral by residuesThink of the branch of $\log z$ defined on $\mathbb{C}\setminus[0,\infty)$ such that $\log(-1)=\pi i$ (and $\log1=0$.) Starting from $z=1$ go around a circle counterclockwise. You travel the path $z=e^{i\pi t}$ with $t$ going from $0$ to $2\pi$. The value of $\log z$ goes then from $0$ to $2\pi i$. Now remember that $z^{1-a}=e^{(1-a)\log z}$. 9h answered Evaluating real improper integral by residues 9h comment Evaluating real improper integral by residuesIt is understood that the sum is over the singularities of the function you are integrating. In this example the only possible values of $a$ are $\pm i$. 1d answered How are the wolfram alpha pikachu curve and others generated? Dec 7 answered Conditional convergence of $\sum_{n=2}^{\infty}\ln\left[1+\frac{(-1)^n}{n^p}\right]$ Dec 5 answered A wave equation with a weird boundary condition Dec 5 answered Find the limit of $a_n = \sqrt[n]{b^n + c^n}$ Dec 5 awarded integration Dec 4 answered Integration involving non-elementary functions Dec 4 revised Finding the maximum number of $x\in\mathbb R$ such that $a^x+b=\lfloor x\rfloor.$Added a proof of the conjecture stated in the answer. Dec 3 reviewed Approve suggested edit on How would I prove that this function is bijective? Dec 3 reviewed Approve suggested edit on Basic math question Dec 3 answered Finding the maximum number of $x\in\mathbb R$ such that $a^x+b=\lfloor x\rfloor.$ Dec 3 comment Calculation of $\sum_{k=0}^\infty \sin(x)^{ki}$But the series is not convergent: $|(\sin x)^i|=1$. Dec 3 comment Calculation of $\sum_{k=0}^\infty \sin(x)^{ki}$Which branch of $\ln$ are you using? Dec 3 comment Prove that there exists an uniformly continuous $g$ such that $f = g$ a.eMay be there is a way to prove it avoiding the Ascoli-Arzela theorem. At first I tried to prove that $f^h$ converges uniformly bounding $\|f^h-f^k\|_\infty$ and using the uniform Cauchy condition, but could not do it. This does not mean that it is not possible. I used the condition $\|f_h-f\|_\infty\to0$ to get $|f(x-y)-f(x'-y)|<\epsilon$. Dec 2 revised For which $L^p[0,1]$, $1\le p < \infty$ does the function $n^\alpha*\chi_{[0,1/n]}$ converge weakly to 0?edited title Dec 2 reviewed Approve suggested edit on On locally small category Dec 2 reviewed Edit suggested edit on Inequality for Euclidean norm Dec 2 revised Inequality for Euclidean normfixed grammar