# Trouble with an index change in Laurent series

1. Mar 6, 2016

### saybrook1

1. The problem statement, all variables and given/known data
Hey guys, I'm just going through a Laurent series example and I'm having trouble understanding how they switched the index on a summation from n=0 to n=1 and then switched the argument from z^(-n-1) to z^n as well as changing the upper limit to -infinity. If anyone could shed some light on that for me I would really appreciate it.

2. Relevant equations
http://imgur.com/0PkgLim

3. The attempt at a solution
I thought that if you changed the index to n=1 then the power on z should just move up one erasing the ^(-1) and i'm not sure how switching the limit to negative infinity changes anything. Thanks for any help.

File size:
14.8 KB
Views:
32
2. Mar 6, 2016

### vela

Staff Emeritus
Try rewriting the summation in terms of $k = -n-1$. What values does $k$ cover when $n$ goes from $0$ to $\infty$?

3. Mar 25, 2016

### saybrook1

Thank you very much :)