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March 11th, 2014, 05:34 PM   #1
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Convergence test using taylor series

Let
L(s,thetaj)=P(s)+Q(s)e^(-theta1*s)+R(s)e^(-theta2*s) be an analytic function. And Let s* be any one of the roots of L(s,thetaj) y and let p be a positive number such taht the only root of L(s,thetaj) contained inside the contour |s-s*|=p is s*.


How can I use the Taylor series in L(s, thetaj) and prove convergence | s - s * | = p ?
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