# Luboš Motl

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bio website motls.blogspot.com location Czech Republic age 40 member for 2 years, 10 months seen Mar 6 at 19:34 profile views 2,407

Hi, I am a string theorist and a publicist.

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 Jun10 comment Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ Oh, I eventually noticed that it's actually the same thing. In that case, I am sure that your result is correct. In the original formula, the whole big ratio in the parentheses should be squared, otherwise it's correct. Jun10 awarded Nice Answer Jun10 answered Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ Jun9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) The four derivatives $\partial f_{1,2} / \partial (x,y)$ are all nonzero at $(1/2,0)$ and the matrix is non-singular over there, so it's clear that in a vicinity of the point, the inverse exists. Jun9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) Maybe they just want an approximate formula for the inverse? I can't imagine how the formulae could simplify. Or maybe you're allowed to use some symbols inside? Something that makes the solution "non-explicit"? Jun9 answered Question about direct sum of function space Jun9 answered A radius for which the inverse of a function is well defined (Inverse Function Theorem) Jun9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) I see, thanks, it's a comma. ;-) Jun9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) Sorry, I may be missing something, but how can you invert a function of two variables? Your function is from $R^2$ to $R$, so it cannot be a simple function, so it can't be (fully) inverted. The inverse function would have to be from $R$ to $R^2$, right? Jun9 comment Finding number of matrices whose square is the identity matrix Hi, every $9\times 9$ matrix $A$ may be brought into the standard form $A=CDC^{-1}$ for a $D$ which is either diagonal or has the Jordan blocks on the diagonal. That's a basic result in algebra. In this form, $A^2 = CDC^{-1}CDC^{-1} = CD^2 C^{-1}$. It should be equal to $I = CC^{-1}$ which implies $D^2=I$. So $D$ has to have $\pm 1$ eigenvalue and one may check that the nondiagonal Jordan blocks would fail to produce $D^2=1$, too. Jun9 revised Finding number of matrices whose square is the identity matrix added 263 characters in body Jun9 answered Finding number of matrices whose square is the identity matrix Jun8 answered What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$? Jun6 revised Bounding ${(2d-1)n-1\choose n-1}$ added 199 characters in body Jun6 revised Bounding ${(2d-1)n-1\choose n-1}$ added 560 characters in body Jun6 answered Bounding ${(2d-1)n-1\choose n-1}$ Jun6 revised Minimum value of $x+4z$ subject to the constraint $x^2+y^2+z^2\leq 2$? added 59 characters in body Jun6 answered Minimum value of $x+4z$ subject to the constraint $x^2+y^2+z^2\leq 2$? Jun6 comment Minimum value of $x+4z$ subject to the constraint $x^2+y^2+z^2\leq 2$? You switch $1$ and $3$ in $F$ which is from $R^3$ to $R$, not the other way around. Jun6 answered Questions about open sets in ${\mathbb R}$