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May
2
comment Calculating this integral: $I=\int_{0}^{\infty}(\log t)\,(\tan^2t)\,\mathrm{d}t$
You have bounds $0$ and $\infty$ in the title but some other numbers in the body, which is it?
Apr
10
comment Help with this combinatorial proof $\sum\limits_{k=1}^nk^2(k-1){n\choose k}^2 = n^2(n-1){2n-3\choose n-2}$ considering $n\ge2$
Where did you get this formula? left-hand side gives $480$ and right hand side gives $160$ for $n=4$...
Apr
10
comment What does this equal? $6\div 2(1+2)$
how does someone get $7$?
Apr
10
comment Are the two integrals equivalent?
Yes they are indeed the same
Apr
5
comment Simple way to see this integral is 0?
See math.stackexchange.com/questions/139393/…
Mar
31
comment $f(x)=x$ if $x$ is rational , $f(x)=1-x$ if $x$ is irrational, at what point this function is continuous?
You beat me to it, +1
Feb
26
comment Finding out the coeffcient next to $x^2$ in $(\cdots(x-2)^2-2)^2\cdots-2)^2$.
I don't know why it is, but it seems the recurrence is $a(n)=20a(n-1)-64a(n-2)$, which gives the solution $(4*16^n-4^n)/3.$
Feb
19
comment Prove that $\sum_i\sum_j a_{ij}=\sum_j\sum_i a_{ij}$
See math.stackexchange.com/questions/497096/…
Oct
23
comment Integral of product of two measurable functions
This is essentially a special case of Holder's inequality.
Oct
22
comment Mean value of the image of an exponentiallly distributed time under a smooth curve
$f(t)$ should be $\phi(t)$ in 3.
Oct
21
comment How prove this $\int_{-\pi}^{+\pi}\cos{(2x)}\cos{(3x)}\cos{(4x)}\cdots\cos{(2005x)}dx>0$
I dont have a solution, just some computation with maple/ WA
Oct
21
comment How prove this $\int_{-\pi}^{+\pi}\cos{(2x)}\cos{(3x)}\cos{(4x)}\cdots\cos{(2005x)}dx>0$
The integral of $\prod_{k=2}^{n}cos(kx)$ seems to be $0$ for values of $n$ congruent to $-1, 0 \mod 4$ and a positive rational fraction of $\pi$ for $1,2\mod 4$
Oct
20
comment Power series $ \sum_{r=1}^{n}x^{r}=\:?$
Almost surely this has been answered here before
Oct
20
comment $\int_{-\infty}^{\infty} \frac{1}{2\pi} \exp\{ -\frac{1}{2} ((y-x)^2 + x^2) \} dx$
square completion
Oct
18
comment use combinatorial reasoning to calculate $ \sum{\binom{100}{a}\binom{200}{b}\binom{300}{c}}$
To add some reference, this is sometimes known as Vandermonde's convolution
Oct
17
comment How find the minimum of the value of $n$ such $n^2\equiv 1\pmod{1007}$
Am i missing someting? $1$ will do
Oct
16
comment Why do we call it a $\sigma$-algebra?
@Did doesn't make more sense does it? unles they were auto referencing to the Bourbaki trive they are$ even then
Oct
16
comment Why do we call it a $\sigma$-algebra?
In French, we even use the word "Tribu", which makes even less sense
Oct
16
comment Is there a fast way to compute coefficient of some term of the product of some series'?
@user100508 Yes there is someting to do in that case, perhaps ask a new question for that particular case.
Oct
15
comment Is there a fast way to compute coefficient of some term of the product of some series'?
@user100508 Using $A*B$ to be the cauchy product of two series, you could derive that it is in fact a convolution. In particular, it is associative, so for $A*B*C$, start by computing $D=A*B$ and then $D*C$. I do not know of a more elegant formula other than the one you'd get arranging all the sums this process give you