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 Jun 21 comment Aysmptotic relation @anon we can't use de l'Hospital rule if we don't know limits of $f$ and $g$ when $x \to +\infty$. Jun 20 comment Integration by means of complex analysis @PeterTamaroff oh, pardon me. Nice job :) Jun 20 comment Integration by means of complex analysis @PeterTamaroff you still use P.V. for cosine which simply can't work. Jun 20 comment Integration by means of complex analysis @PeterTamaroff I've got some link for you math.stackexchange.com/questions/9402/… btw today I discovered that here is something like FAQ for topics :D Jun 20 answered Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$ Jun 20 comment infinite series involving harmonic numbers and zeta @Chris you mean double summation $\sum_n \sum_m$? I don't think so, because when treating this sum elementary $H_n$ is sum itself. Jun 19 awarded Mortarboard Jun 19 comment Question regarding Kuhn-Tucker multiplier Pleas use LaTeX syntax and dollar signs for math input. Jun 19 revised Question regarding Kuhn-Tucker multiplier I've made some formulas look nicer. Jun 19 suggested approved edit on Question regarding Kuhn-Tucker multiplier Jun 19 comment Evaluating Integral with Residue Theorem @Synia sure, if the residues sum up to $0$ why not? Consider for example function $g(z) = \frac{1}{z} - \frac{1}{z-1}$. Then ${\rm Res}_{z=0} g(z) = 1$ and ${\rm Res}_{z=1} g(z) = -1$ so when integrating along adequate contour the integral will be $0$. Jun 19 answered infinite series involving harmonic numbers and zeta Jun 19 comment Integration by means of complex analysis @robjohn right. In the chat room I proposed to have $I'(t) = \int_0^{+\infty} \frac{\cos tx}{1+x^2}\, dx$ than $I(t) = \int_0^{+\infty} \frac{\sin tx}{x(1+x^2)}\,dx$ and ODE is $I''(t) - t^2 I(t) = - \frac{\pi}{2}, \; I(0)=0, I'(0) = \frac{\pi}{2}$ but there is a problem how to solve it in a nice way :) Jun 19 comment Integration by means of complex analysis Let's take $$F(a) = \int_0^{+\infty} \frac{\cos (a+x)}{1+x^2} \, dx$$ then we have the desired ODE: $F''(a) + F(a) = 0$ But the problem is to choose initial conditions :| . Jun 19 revised Evaluating Integral with Residue Theorem Fixing formating Jun 19 answered Evaluating Integral with Residue Theorem Jun 19 suggested approved edit on Evaluating Integral with Residue Theorem Jun 19 answered Evaluating $\lim_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ Jun 19 revised How integrals are computed? Use LaTeX to write equations Jun 19 suggested approved edit on How integrals are computed?