I am reading a chapter on Complex Functions, Laplace Transforms & Cauchy Riemann (as part of Control theory) And I don't understand how they arrive at a particular part. [ I tried to type it out in tex, but it takes way too much time so uploaded a screenshot to flickr] [PLAIN]http://www.flickr.com/photos/66943862@N06/6093176535/ [Broken] Here is a http://www.flickr.com/photos/66943862@N06/6093176535/" [Broken] I understand how you get to Eqn1 & Eqn2. But how does it add up to Equation3? Can someone explain? Also, I don't understand why it's not analytic at s = -1?