Grigory M
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 Dec24 comment Does a four-variable analog of the Hall-Witt identity exist? Related: negative answer @ MO Dec24 comment Does a four-variable analog of the Hall-Witt identity exist? Dec23 comment The close form expression of a Pfaffian $\operatorname{Pf}(1/(x_j-x_i))$ can be computed using Cauchy determinant identity, perhaps Dec22 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... Dec20 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 Dec20 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/… Dec20 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, $32x^5+16x^4-32x^3-12x^2+6x+1=0$)... Dec19 comment Explanations of the Euler's continued fractions to compute exponential (slightly) related: Continued fraction for $\frac{1}{e-2}$ Dec19 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 Dec19 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? Dec19 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? Dec18 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) Dec18 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. Dec18 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? Dec18 comment Quaternion Projective Space Dec18 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) Dec15 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?.. Dec15 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. Dec13 comment Moves for regular homotopies of immersions of $S^1$ in the plane AFAIR two such immersions are equivalent iff they have the same winding number (H. Whitney. On regular closed curves in the plane), no? Dec13 comment CW-complex with zero boundary operators Cf. definition of formal dg-algebra, btw