KvanTTT
Reputation
380
Top tag
Next privilege 500 Rep.
Access review queues
 Feb 16 comment Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$ Maybe this formula is better and shorter? $$-\gamma - \ln {\frac {8 \pi ^ 2} {\Gamma (\frac {1} {4}) ^ 4 }}$$ Feb 13 comment Surprising identities / equations It looks interesting. In other words: $^{2}3 + ^{2}4 + ^{2}3 + ^{2}5 = 3435$, where $^{b}a$ is tetration. Nov 27 comment Why does $1+2+3+\cdots = -\frac{1}{12}$? @GottfriedHelms, I don't know. Probably there is a way to evaluate not only c coefficient (-1/12) of this parabola, but a and b too. It works only with infinite number of points (excel can process only finite set). Sep 27 comment Why does $1+2+3+\cdots = -\frac{1}{12}$? @ChrisCulter, yep, it's my additions. I updated the answer. Feb 16 comment Calculate $\lceil \frac{n}{log_2k} \rceil; n \geqslant 1, k \geqslant 2$ with only integer functions @abstractnature, I typed in latex by myself with help of MathJax basic tutorial and quick reference. Also I used Detexify2 service for getting '\' code in latex. Why did you ask about it? Nov 4 comment Solid angle between vectors in n-dimensional space @Martin, you are right. Sorry for my mistake. I meant Exterior product there and I've already fixed my answer with it. Oct 10 comment A generalized (MacLaurin's) average for functions It's also an interesting: Is your observation related to Harmonic average? Oct 3 comment Definite integral of tetration between $0$ and $1$ Yes. Did you surprise because of this series expansion is trivial for you? :) Oct 3 comment How to plot N points on the surface of a D-dimensional sphere roughly equidistant apart? I guess N coordinates must be generated with any Gaussian random and after that resulting vector have to be normalized and multiplied on the R. Oct 3 comment How to plot N points on the surface of a D-dimensional sphere roughly equidistant apart? No, I mean $N \le D + 1$, that is all simplexes with such dimensions. For example, for 3D sphere segment there are segment (2 vertices), triangle (3 vertices) and tetrahedron (4 vertices). But you are right: this method not suitable for $N > D + 1$ case. Oct 3 comment Definite integral of tetration between $0$ and $1$ It's great, but what ablout case of definite integral inside of $[0; 1]$ interval? Sep 28 comment How do I compute multinomials efficiently? It's great! I updated my answer with this formula. Sep 26 comment Solid angle between vectors in n-dimensional space I saw this formulas. But i don't know how to implement their to vectors case. Sep 25 comment Inverse function of $y=W(e^{ax+b})-W(e^{cx+d})+zx$ Could you explain background of this task, if it's not a secret. Sep 21 comment What is the geometric, physical or other meaning of the tetration? @joriki, sorry for my language. I mean is there physics applications of tetration? Or it's only have theoretical meaning. For example, first and secod derivatives of function is velocity and acceleration in terms of kinematics. Fermat's Last Theorem has no applications but has a great theoretical value. Sep 20 comment Generalized rotation matrix in N dimensional space around N-2 unit vector Thank you, @RobertIsrael. But i don't understand how to switch from your explanation with two orthogonal vectors to rotation around N-2 dimensional plane? Can you show it on Rodrigues' Rotation Formula? Sep 16 comment Generalized rotation matrix in N dimensional space around N-2 unit vector Ok, but is there efficient algorithm for finding every matrix item, based on special numbers, permutations or something else, exists?