2,148 reputation
620
bio website qoqosz.net
location Poland
age 25
visits member for 2 years, 5 months
seen Sep 14 at 15:55

I'm just a physics student.


Nov
6
comment A closed form for the sum $\sum_{n=1}^{\infty}\left(\frac{H_n}{n}\right)^2$
Check this one: ams.org/journals/proc/1995-123-04/S0002-9939-1995-1231029-X/…
Nov
6
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.
Nov
5
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/…
Nov
5
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 ($z > 0$).
Nov
2
comment Integration in n-spherical coordinates
Thanks, I've already got an answer on physics.SE: physics.stackexchange.com/questions/83103/…
Oct
13
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?
Jun
26
comment Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?
@André indeed, thanks.
May
24
comment Improper integral and special functions
@RaymondManzoni thank you.
Jul
26
comment Sum equals integral
Thank you for your answer. These references are very helpful.
Jul
16
comment Inequality Related to $\arctan$ function
@Fabian except $x = 0$ ;)
Jul
16
comment How do I calculate the limit of this integral?
Your question is related to this one: math.stackexchange.com/questions/160248/…
Jul
15
comment Sum equals integral
Actually I would be more interested in neat examples rather than general methods for finding such functions.
Jul
14
comment Sum equals integral
@RossMillikan If summation of a series would range also from $-\infty$ to $+\infty$ than ${\rm sinc}$ is a nice example.
Jul
9
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.
Jul
9
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: $$\int_0^1 \frac{f'(x)}{1 + f^2 (x)} \cdot \frac{dx}{f'(x)} \le \frac{\arctan f(1)}{f'(1)} \le \frac{f(1)}{f'(1)}$$
Jun
26
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: $$\frac{\partial \phi}{\partial x} = \frac{\partial \phi}{\partial r} \frac{\partial r}{\partial x} + \frac{\partial \phi}{\partial \theta} \frac{\partial \theta}{\partial x}$$
Jun
26
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.
Jun
25
comment A linear differential equation
@rubik ok, here it goes.
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.