Ah thanks, I never really knew what the first parameter was in matlabs lambertw function.
Out of interest, is there some closed form expression for W(x)?
I found the taylor expansion W_0 (x) = \sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!}\ x^n
but it doesn't have an imaginary part so surely can't...
Did you use the W-function to get that result? I've been hoping to find an alternate method to solve this which could maybe lead to a closed form expression.
As of now, the expansion for e^x isn't getting me very far.
Also, not that it's of much use, e^x=x also implies e^e^e^...e^x = x =...
-.- faceplants. I overcomplicated that way too much.
vanesch, your proof makes it seem certain now, whereas when I first posted the thread, I wasn't entirely sure it was true myself. Thanks :)
Any chance you could prove this (g = v^2/r)? I tried proving it myself but kept getting slightly differing results. My teacher won't admit he's wrong on the basis of a statement I can't prove. :)
And that is quite interesting. Is it not simply because the parabola and the circle share a...
Surely this 'proof' just states that M doesn't exist so it is in {¬K} which contains all that is not in {K}
Then when you debunk the original statement as 'absurd', you claim {K} is not all that is known so {¬K} is no longer all that isn't real, it also contains elements whose reality are...
If you're thinking of the object moving along horizontally inside the cylinder and coming out the end, I think I may have explained it badly. The object is moving in a perfect circle vertically, it never leaves the cylinder. I called it a cylinder rather than just a circle to show that the...
Me and my mathematics teacher are in a (trivial) debate as follows;
My argument is that an object moving in vertical circular motion on the inside of a cylinder can instantaneously experience a reaction force of zero at the top of the circle.
He argues that as soon as reaction force from...
It probably isn't at all difficult to solve for x, with the exponent interpreted in any way
I'd say your problem is finding the log base 264 button on that cash machine.
Surely if the robot has passed over each square exactly twice, the robot has followed some path from the first square to the last, and the last square he stands on changes to point back to the square he came from.
This means he will follow that same path to get back to the start and will have...
x^{2} = y^{2} \Rightarrow |x| = |y|
Isn't this correct though?Also, MATLAB gave the error 'Warning: Explicit solution could not be found.' when trying to solve the equation.
And Microsoft Math gave x=1, which is clearly incorrect
Okay, before you scream x = ∞, I'm finding the complex solution to the problem.
I'll show you my working so far, maybe you'll see something I missed.
First let x = a+bi
e^(a+bi) = a+bi
e^a * e^bi = a+bi
Applying Euler's identity
e^a*cos(b) + ie^a*sin(b) = a+bi
e^a*cos(b) = a
e^a*sin(b) = b...
I really didn't know how to word the title so sorry if it's a little confusing.
And I didn't know whether to post this in number theory or not but ah well.
The other day, I started thinking about this and I was just wondering if it had been done before or if it's even correct;
Half of all...