I am trying to understand the idea of annulus of convergence. This is the example I have been looking at but it has me completely stumped.
[∞]\sum[/n=1] (z^n!)(1-sin(1/2n))^(n+1)! + [∞]\sum[/n=1] (2n)!/[((n!)^2)(z^3n)]
All of the examples I have worked on in the past have been...
Edit: The latex was not loading but now I see what you mean. I apologize if this sounds ignorant but I did not think e^(i*zn) was bounded. If you are saying I should show it is then I assume it can be.
When I think of this sequence I must be seeing it all wrong. could you give any...
Homework Statement
Describe the largest region in which g(z) = 1/[Log(z)-(i*pi)/2] is analytic?
The Attempt at a Solution
Analytic is where the cauchy-euler equations hold, so I tried to take the partials to and set them equal so I could define a domain. I am not sure if the partials...
I thought I had gotten to the point of it being a big algebra problem but the wall I am hitting is what to do to it. Is there some way to connect conj(z)/z to the unit circle?
Yes, I do know the B-W theorem. I looked at it but it applies to bounded sequences. This sequence is only bounded below and only on the I am part. I suppose since you asked you see a way it is still applicable.
It was my understanding e^z forms a circle in the complex. Is this what you mean?
Let <zn> be a sequence complex numbers for which Im(zn) is bounded below.
Prove <e^(i*zn)> has a convergent subsequence.
My question on this is what possible help could the boundedness of the Im(zn) to this proof and what theorem might be of help?