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 Jun 23 comment A linear differential equation @ZevChonoles maybe I should just delete this topic? I didn't know that posting some (imho) interesting problems will be such a trouble. Jun 23 comment A linear differential equation @ZevChonoles so here goes the tag. I think submitting my own solution would spoil the problem a bit. Jun 23 revised A linear differential equation edited tags Jun 23 comment A linear differential equation @ZevChonoles I know this poem, as well as a solution. I though some of math.SE users would find this problem interesting :| Jun 23 asked A linear differential equation Jun 23 comment Fourier transformation of $x^2 e^{-\lambda x}$ @Mercy as I mentioned it only exists in distributional sense. For normal functions the integral obviously diverges. Jun 23 comment Fourier transformation of $x^2 e^{-\lambda x}$ In the distributional sense, using differentiation under the integral sign you'll get sth like $\delta''(\epsilon + i \lambda)$. Jun 23 comment Sum inequality: $\sum_{k=1}^n \frac{\sin k}{k} \le \pi-1$ Possibly related: math.stackexchange.com/questions/13490/… Jun 22 comment Prove that: $\int_{0}^{1} \frac{x^{4}\log x}{x^2-1}\le \frac{1}{8}$ Practically this solution uses @PeterTamaroff work, without it you could as well write right away $\frac{\pi^2}{8} - \frac{10}{9} \le \frac{1}{8}$ :/ Jun 22 revised Prove that: $\int_{0}^{1} \frac{x^{4}\log x}{x^2-1}\le \frac{1}{8}$ added 209 characters in body Jun 22 revised Prove that: $\int_{0}^{1} \frac{x^{4}\log x}{x^2-1}\le \frac{1}{8}$ edited body Jun 22 answered Prove that: $\int_{0}^{1} \frac{x^{4}\log x}{x^2-1}\le \frac{1}{8}$ Jun 22 answered Computing the derivative from the definition Jun 22 answered Integral as a limit of a sum Jun 22 answered How to calculate first variation of length of curve? Jun 22 answered Prove that: $\frac1{20}\le \int_{1}^{\sqrt 2} \frac{\ln x}{\ln^2x+1} dx$ Jun 21 comment $\int f(x) dx$ is appearing as $\int dx f(x)$. Why? @AppliedImagination actually I study physics :) Jun 21 comment $\int f(x) dx$ is appearing as $\int dx f(x)$. Why? The argument I heard and which is quite convincing is that in physics $f(x)$ can have very long form. So in order not to forget about $dx$ we write it first :) Jun 21 comment Limit of sum with binomial coefficient One way is to consider integral: $$\frac{1}{2i} \int_\gamma \sqrt{ \frac{\Gamma (n+1)}{\Gamma (n+1 - z) \Gamma (z+)}} \frac{1}{\sin \pi z} \, dz$$ where $\gamma$ is a rectangle with corners in $-\frac{1}{2} \pm ib$ and $n+\frac{1}{2} \pm ib$ than take limit $n, b \to +\infty$ which requires some manipulations along the road. Jun 21 comment Aysmptotic relation @anon sorry, I meant $F$ and $G$.