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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?

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?

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