We have , expansion valid for or equivalently for .
Hi there. I have to find the Laurent series for
So what I did was calling , I don't know if this is right.
Then:
And then back to z:
I have to make the series for |z|>2, but I see that it gives the same as when I centered the series in zero, so I think I'm doing something wrong.
What's the difference for I just don't see it. I've proceeded exactly as you did when finding the Laurent series for this same function centered at zero, and I get the same series that we've found here, with exactly the same expressions for the modulus.
If I take then I get:
That's the Taylor part, the other gives the same that you found.
Let us see, you have completed the Laurent expansion valid for that is, centered at which is the same than the Taylor expansion (there is no principal part). On the other hand we have completed the Laurent expansion valid for that is , in another region centered at . Right? Then, in the second case we also say that we have the expansion centered at because is a neighborhood of .
Thank you Fernando I was reading some of your works by the way. That poly-dimensional time that you've proposed, and the movement of movements it sounds like a really interesting thing. It's not something that we should discuss right here, I can't discuss it anyway, but I wanted to mention it :P
Bye bye! see you around.