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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
20
answered Are there any open mathematical puzzles?
Oct
19
answered Determine $a<0$ such that $\int_a^0 f(x) dx = f(a)$
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
reviewed Looks OK Residue at $0$ of $\frac{1-\cos z}{z^4}$
Oct
16
reviewed Approve suggested edit on Fuchsian Groups: A counterexample
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
Oct
15
answered Is there a fast way to compute coefficient of some term of the product of some series'?
Oct
15
reviewed No Action Needed probability without replacement and unknown number in urn
Oct
15
comment How do I reduce this: $\frac{2}{x\ln(4)}\quad ?$
don't, mostly everyone stumbles at one point or another onto something quite obvious.
Oct
15
comment Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$
@user64494 What I gave above evaluates to $1.8660736602994162541590468656767972604020575060868...$
Oct
15
comment Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$
Probably, Maple gives $(1/2)\pi\sqrt{2}(\sin(1/2)*BesselJ(0, 1/2)-\cos(1/2)BesselY(0, 1/2))$
Oct
15
comment Gaussian density function satisfies $y'=-xy$. Coincidence?
Have a look at digilib.lib.unipi.gr/spoudai/bitstream/spoudai/542/1/…
Oct
15
reviewed Looks OK How do I reduce this: $\frac{2}{x\ln(4)}\quad ?$
Oct
15
answered How do I reduce this: $\frac{2}{x\ln(4)}\quad ?$