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54m
answered Square root of a matrix as it relates to the identity
59m
answered Series that converges to $1$ slowly
2h
answered What does P(X=Y) mean?
2h
comment Independence and expected value
Or if you want $X$ and $Y$ to be non-negative as well, take $X$ uniform on $[0,2]$ and $Y = (X-1)^2$.
4h
answered Prove that if a function has an isolated singularity at $z_0$, then its derivative also has an isolated singularity at $z_0$
4h
answered Find the number of vertices n of the tree?
4h
comment Functional Equation: $f(x^2-y^2)=xf(x)-yf(y)$
See Wikipedia.
4h
answered Functional Equation: $f(x^2-y^2)=xf(x)-yf(y)$
5h
revised Let $f(x)=x^3-3x+1$.Find the number of distinct real roots of $f(f(f(x)))=3$
added 438 characters in body
6h
answered Let $f(x)=x^3-3x+1$.Find the number of distinct real roots of $f(f(f(x)))=3$
16h
answered Under what condition on matrix $Q$ we have $tr(AQ)=tr(BQ)$
17h
answered Is there a graph that has 7 vertices and each vertex has a degree of $2,2,3,5,5,5,6$?
18h
answered Have any property of square to make below problem reasonable?
18h
comment Definition of ordered ring flawed?
But it doesn't satisfy the first property: $1 \le 2$ but $1+1 > 2+1$.
22h
answered Differential Equation - Where does the solution end?
22h
comment Closed-Form solution for system of simple nonlinear equations
Also, if you're really interested in $N \approx 10,000$, algebraic methods are likely to be essentially useless.
22h
revised Closed-Form solution for system of simple nonlinear equations
added 250 characters in body
23h
comment Closed-Form solution for system of simple nonlinear equations
I suspect this might not be well-received at MO. First of all, "analytical" or "analytic" is not the right word. To a mathematician, "analytic" means "locally given by a convergent Taylor series". What you mean is more like "closed form", but that's still ambiguous: exactly what kinds of special functions are you going to allow? For example, some high-order polynomials can be solved by generalized hypergeometric functions, theta functions, etc. Would you be happy with that?
1d
comment Solving equation of form $x = -a/ln(bx)$
I mean that you made a mistake. The solution to the equation you wrote is $-a/W(-ab)$, not $-a/W(-a/b)$.
1d
answered Solving equation of form $x = -a/ln(bx)$