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 Nov6 comment A closed form for the sum $\sum_{n=1}^{\infty}\left(\frac{H_n}{n}\right)^2$ Nov6 comment Integral $\int_{-\infty}^{\infty}\frac{\mathrm dx}{(ax^2+2bx+c)^{\alpha}}$ It's one of the Beta function (en.wikipedia.org/wiki/Beta_function) representations. If you substitute $p = u^2$ it will become more apparent. Nov5 comment evaluation of $\int\frac{x^2}{\left(1+x^4\right)\sqrt{1+x^4}}dx$ If you are looking for an elementary solution - there isn't one due to: encyclopediaofmath.org/index.php/… Nov5 comment Integral from zero to infinity of $\int_0^{\infty}\frac{(1-e^{-\lambda z})}{\lambda^{a+1}} d \lambda$ @ghiasi This condition appears when you check when $\int_0^z t^{a-1} dt$ and $\int_0^{+\infty} x^{-a} e^{-x} dx$ converge ($z > 0$). Nov2 comment Integration in n-spherical coordinates Thanks, I've already got an answer on physics.SE: physics.stackexchange.com/questions/83103/… Oct13 comment Divergence in spherical coordinates @user8268 So if $\vec F$ is defined as: $F^\alpha = \frac{\partial f (u(r, \theta, \phi), \ldots)}{\partial (\nabla_\alpha u)}$ and I compute $\nabla_\alpha u$ as $(\partial_r u, \frac{1}{r} \partial_\theta u, \frac{1}{r \sin \theta} \partial_\phi u)$ than which formula for $\nabla \cdot \vec{F}$ should I use? The first one? Jun26 comment Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$? @André indeed, thanks. May24 comment Improper integral and special functions @RaymondManzoni thank you. Jul26 comment Sum equals integral Thank you for your answer. These references are very helpful. Jul16 comment Inequality Related to $\arctan$ function @Fabian except $x = 0$ ;) Jul16 comment How do I calculate the limit of this integral? Your question is related to this one: math.stackexchange.com/questions/160248/… Jul15 comment Sum equals integral Actually I would be more interested in neat examples rather than general methods for finding such functions. Jul14 comment Sum equals integral @RossMillikan If summation of a series would range also from $-\infty$ to $+\infty$ than ${\rm sinc}$ is a nice example. Jul9 comment Find the functions family that satisfies the inequality $\int_0^1 \frac{dx}{1+f^{2}(x)} <\frac{f(1)}{f'{(1)}}$ @Mercy it is derivative which is not increasing. Jul9 comment Find the functions family that satisfies the inequality $\int_0^1 \frac{dx}{1+f^{2}(x)} <\frac{f(1)}{f'{(1)}}$ Here's my first though: If we assume that: $f'$ is continuous and not increasing; $f'(1) \neq 0$; $f(0) = 0$; $f(1) \ge 0$, than: $$\int_0^1 \frac{f'(x)}{1 + f^2 (x)} \cdot \frac{dx}{f'(x)} \le \frac{\arctan f(1)}{f'(1)} \le \frac{f(1)}{f'(1)}$$ Jun26 comment gradient in polar coordinate by changing gradient in Cartesian coordinate You wrote: $$\frac{\partial \phi}{\partial x} = \frac{\partial \phi}{\partial r} \frac{\partial r}{\partial x}$$ instead of: $$\frac{\partial \phi}{\partial x} = \frac{\partial \phi}{\partial r} \frac{\partial r}{\partial x} + \frac{\partial \phi}{\partial \theta} \frac{\partial \theta}{\partial x}$$ Jun26 comment Two sums for $\pi$ @daniel I missed the link :( Ok, I'll try to make it more complete and then I'll post it there. Jun25 comment A linear differential equation @rubik ok, here it goes. Jun23 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. Jun23 comment A linear differential equation @ZevChonoles so here goes the tag. I think submitting my own solution would spoil the problem a bit.