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| bio | website | qoqosz.net |
|---|---|---|
| location | Poland | |
| age | 24 | |
| visits | member for | 1 year |
| seen | Mar 29 at 12:10 | |
| stats | profile views | 181 |
I'm just a physics student.
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Jul 26 |
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Sum equals integral Thank you for your answer. These references are very helpful. |
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Jul 16 |
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Inequality Related to $\arctan$ function @Fabian except $x = 0$ ;) |
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Jul 16 |
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How do I calculate the limit of this integral? Your question is related to this one: math.stackexchange.com/questions/160248/… |
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Jul 15 |
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Sum equals integral Actually I would be more interested in neat examples rather than general methods for finding such functions. |
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Jul 14 |
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Sum equals integral @RossMillikan If summation of a series would range also from $-\infty$ to $+\infty$ than ${\rm sinc}$ is a nice example. |
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Jul 9 |
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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. |
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Jul 9 |
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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: $$\int_0^1 \frac{f'(x)}{1 + f^2 (x)} \cdot \frac{dx}{f'(x)} \le \frac{\arctan f(1)}{f'(1)} \le \frac{f(1)}{f'(1)}$$ |
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Jun 26 |
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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: $$\frac{\partial \phi}{\partial x} = \frac{\partial \phi}{\partial r} \frac{\partial r}{\partial x} + \frac{\partial \phi}{\partial \theta} \frac{\partial \theta}{\partial x}$$ |
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Jun 26 |
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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. |
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Jun 25 |
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A linear differential equation @rubik ok, here it goes. |
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Jun 23 |
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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. |
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Jun 23 |
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A linear differential equation @ZevChonoles so here goes the tag. I think submitting my own solution would spoil the problem a bit. |
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Jun 23 |
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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 :| |
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Jun 23 |
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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. |
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Jun 23 |
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Fourier transformation of $x^2 e^{-\lambda x}$ In the distributional sense, using differentiation under the integral sign you'll get sth like $\delta''(\epsilon + i \lambda)$. |
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Jun 23 |
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Sum inequality: $\sum_{k=1}^n \frac{\sin k}{k} \le \pi-1$ Possibly related: math.stackexchange.com/questions/13490/… |
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Jun 22 |
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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 $\frac{\pi^2}{8} - \frac{10}{9} \le \frac{1}{8}$ :/ |
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Jun 21 |
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$\int f(x) dx $ is appearing as $\int dx f(x)$. Why? @AppliedImagination actually I study physics :) |
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Jun 21 |
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$\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 :) |
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Jun 21 |
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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. |
