/sci/ - Science & Math

<div class="math">\int_{\int_{\int_{\int_{\int}^{\int}}^{\int_{\int}^{\int}}}^{\int_{\int_{\int}^{\int}}^{\int}}}^{\in
t_{\int_{\int}^{\int}}^{\int_{\int}^{\int}}} \int \mathrm{d} \int</div>

<span class="math">∱∳∲[/spoiler]

<span class="math"> \Gamma(z) = \displaystyle \int_0^\infty e^{-t}t^{z-1}dt [/spoiler]

<div class="math">\displaystyle\int e^{x^{2}} dx</div>

<div class="math">\displaystyle \int dx</div>

<div class="math">\int_{\int_{\int_{\int_{\int_{\int_{\int}^{\int}}^{\int_{\int}^{\int}}}^{\int_{\int_{\int}^{\int}}^{
\int_{\int}^{\int}}}}^{\int_{\int_{\int_{\int}^{\int}}^{\int_{\int}^{\int}}}}}^{\int_{\int_{\int_{\i
nt_{\int}^{\int}}^{\int_{\int}^{\int}}^{\int_{\int_{\int}^{\int}}^{\int_{\int}^{\int}}}}}}^{\int}}}^
{\int_{\int_{\int}^{\int}}^{\int_{\int}^{\int_{\int_{\int_{\int}^{\int}}^{\int_{\int}^{\int}}^{\int_
{\int_{\int}^{\int}}^{\int_{\int}^{\int}}}}}}}</div>

<div class="math">\int_0^{2\pi}e^{\cos\theta}\cos(n\theta-\sin\theta)d\theta = \frac{2\pi}{n!}</div>

<div class="math">\int_0^{\infty}e^{ikx}dx</div>

>>4460485
Just curious, how would you go about evaluating that? That's an interesting result.

>>4460481

I see your integral, and I approximate it with Simpson's rule

>>4460489
is that half a delta function? I've only seen that over all R.

>>4460491
It might be something he pulled out of his ass... are those brackets all in the right places?

lets see you faggots do this
<div class="math">\int_0^\pi \log\left( 1-2\alpha \cos x + \alpha^2 \right) \mathrm{d} x</div>

>>4460504
What's alpha represent?

>>4460513

>>4460485
wtf, I just checked that in MATLAB - it works up to at least N = 20...

>>4460496
<div class="math">\int_0^{\infty}e^{ikx}dx=\pi\delta(k)+\frac{i}{k},</div>
where <span class="math">\frac{i}{k}[/spoiler] is defined in a sense of Cauchy principal value

>>4460515
>lol you're confused by notation you've not encountered yet
Is it a variable?

>>4460504
<span class="math">2\pi\ln\alpha[/spoiler]
I looked it up though, I remember seeing it on a math contest I took a year or two ago. Pretty clever ways of doing it.

>>4460504

is that log base ten or natural log

>>4460557
HURRRFAAADURRRRRRRRRRRRRRRRRRRRRRRRRRRRR

>>4460531
It's crystal clear that it is a constant.
>>4460557
The natural logarithm is really the only interesting one so why mention any other?

>>4460582

I understand why it's safe to assume that log means the natural log in higher level math, but why not just use ln?

>>4460491
>how would you go about evaluating that?
You extend it into the complex plane and do some complex analysis. Can't remember the details.

>>4460668
Oh god that sounds like a bitch.

>>4460496
looks like a Fourier transform of the Heaviside/step function