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Dec
28
asked Finding the number of distinct $m$-tuples of distinct numbers whose product is $n$.
Dec
27
comment Closed form for $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2+a^2}$
@RonGordon are there any restrictions on $f(n)$ so that the first result holds? It seems nonsensical if $f(n)$ is entire.
Dec
21
comment Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?
Thank you. In this case, is it possible to easily calculate the integral directly from the beta limit, or is the above method much easier?
Dec
21
comment Understanding $n \left(\frac{2n \choose n}{4^n}\right)^2$ for large $n$
en.wikipedia.org/wiki/Central_binomial_coefficient#Properties See property $2$.
Dec
21
accepted Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?
Dec
20
comment Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?
Thanks very much for answering thoroughly. So is the crux of the existence of the limit that although the limit of a function may exist, the limit of its derivative may exist?
Dec
16
comment Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?
@gammatester Thank you, although my question boils down to finding a nicer form for that limit and (even if the prior isn't possible) to prove that the limit equals $\frac{-1}{2}\zeta(4).$
Dec
16
comment Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?
@gammatester wolframalpha.com/input/…. It seems that the integral is equal to the limit, although the factor of $2$ before $2I$ was incorrect.
Dec
16
revised Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?
added 194 characters in body
Dec
15
asked A closed form for $\sum_{i\cdot j^k=n}(-1)^i$?
Dec
15
answered Prime sum identity
Dec
12
asked Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?
Dec
9
comment $1/i=i$. I must be wrong but why?
Such simplifications only hold when you're dealing with real numbers.
Dec
9
comment Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$
@MhenniBenghorbal, how exactly did you take the beta function limit (excellent answer, by the way)?
Dec
9
comment convex polygon and vectors
Okay, for arbitrary non-collinear $\mathbb{a,b}$?
Dec
9
comment Show that for $0<t<1$, $\log\sin (t\pi)=\log(t\pi) + \sum_{n=1}^\infty\log\left(1-\frac{t^2}{n^2}\right)$
Sorry, didn't read the last part!
Dec
9
comment convex polygon and vectors
Do you want it proven for the displayed polygon or an arbitrary one (in the latter case I think it's impossible)?
Dec
7
accepted Closed form for $\int_0^1 \frac{x^a dx}{(1+x^b)^c}$.
Dec
6
asked Closed form for $\int_0^1 \frac{x^a dx}{(1+x^b)^c}$.
Dec
6
revised Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
edited title