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Dec
25
comment “Why” is $[\mathbb{C}:\mathbb{R}] < \infty$?
For one thing, any polynomial of odd degree has a real root...
Dec
24
comment Solving 5th degree or higher equations
One way to prove this, btw, is Lagrange inversion formula.
Dec
24
comment Does a four-variable analog of the Hall-Witt identity exist?
Related: negative answer @ MO
Dec
24
comment Does a four-variable analog of the Hall-Witt identity exist?
See also lamington.wordpress.com/2011/11/20/the-hall-witt-identity
Dec
23
comment The close form expression of a Pfaffian
$\operatorname{Pf}(1/(x_j-x_i))$ can be computed using Cauchy determinant identity, perhaps
Dec
22
comment Lie algebra of Derivations as a functor?
$\operatorname{Der}(A,M)$ ($M$-valued derivations) is a functor in $M$. As for $\operatorname{Der}(A,A)$, it's in a sense an algebraic version of tangent bundle...
Dec
20
comment Triple Euler sum result $\sum_{k\geq 1}\frac{H_k^{(2)}H_k }{k^2}=\zeta(2)\zeta(3)+\zeta(5)$
Related: math.stackexchange.com/q/606070
Dec
20
comment What comes after $\cos(\tfrac{2\pi}{7})^{1/3}+\cos(\tfrac{4\pi}{7})^{1/3}+\cos(\tfrac{6\pi}{7})^{1/3}$?
(Re: What Ramanujan formula) see (3.8) and (3.18) in maa.org/sites/default/files/pdf/upload_library/22/Ford/…
Dec
20
comment What comes after $\cos(\tfrac{2\pi}{7})^{1/3}+\cos(\tfrac{4\pi}{7})^{1/3}+\cos(\tfrac{6\pi}{7})^{1/3}$?
All cosines in (2) are roots of a (rational) cubic equation. So one can use Ramanujan's formula for the sum of cubic roots of roots of a cubic equation and obtain (2). All cosines in (3) are of course roots of a quintic equation (namely, $32x^5+16x^4-32x^3-12x^2+6x+1=0$)...
Dec
19
comment Explanations of the Euler's continued fractions to compute exponential
(slightly) related: Continued fraction for $\frac{1}{e-2}$
Dec
19
comment How to prove $H^2(\mathfrak{g}, J(\mathfrak{g}))\neq0$, where $J(\mathfrak{g})$ is the augmentation ideal of $\mathfrak{g}$?
repost @ MO: mathoverflow.net/q/83169
Dec
19
comment Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
I'm not sure I understand — certainly you won't be satisfied $\frac27(1+2\sum\eta(2k)2^{-2k})$ — but what's the question exactly then? Anyway, first question is, what is $\sum\zeta(2k)x^{2k}$ and $\sum\eta(2k)x^{2k}$ — do you happen to know answers?
Dec
19
comment Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
There are lots and lots of identities of this type. Have you read answers to your previous question? This one can be solved in exactly the same manner. What have you tried anyway?
Dec
18
comment proof that $PSL(2,\mathbb{R})$ is $SO^+(2,1)$
Related: math.stackexchange.com/q/491455 (a map from SO(1,3) to PSL(2,C) etc)
Dec
18
comment Functors that are the homology of a chain complex
@ZhenLin $K(A,n)$ can be defined as $B^nA$ (or using Dold–Puppe). In this construction it's a topological abelian group, so $[X,K(A,n)]$ clearly is an abelian group. Now the question is why this homological functor can be lifted to a triangulated functor to $D(Ab)$, something like this.
Dec
18
comment Proving that $\left(\frac{\pi}{2}\right)^{2}=1+\sum_{k=1}^{\infty}\frac{(2k-1)\zeta(2k)}{2^{2k-1}}$.
Interesting. But why first equality holds?
Dec
18
comment Quaternion Projective Space
Related: What is the Cayley projective plane?
Dec
18
comment Conditions for a Topological space to be a Spectrum
Being spectrum is an extra structure, not just a condition (i.e. one should fix all deloopings)
Dec
15
comment Limit of $\sum_{i=1}^n \left(\frac{{n \choose i}}{2^{in}}\sum_{j=0}^i {i \choose j}^{n+1}\right)$
Have you tried using Stirling's approximation?..
Dec
15
comment Linear structure on the category of formal groups
You're talking about 1-dimensional FG, right? Because in general FG over R is not isomorphic to additive FG.