Analytic Continuation [k] Suppose we are given the power series expansion f(z) = - which converges...

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Analytic Continuation [k] Suppose we are given the power series expansion f(z) = -Σ which converges for |z| < 1. Sum this series and derive a power series expansion for the resulting function about the point z = -1/2. What is the radius of convergence of this series? Repeat for expansions about z = 1/2 and z = 3/4. Discuss the complication that may arise when analytically continuing to the point z = 2. Analytic Continuation [k] Suppose we are given the power series expansion f(z) = -Σ which converges for |z| < 1. Sum this series and derive a power series expansion for the resulting function about the point z = -1/2. What is the radius of convergence of this series? Repeat for expansions about z = 1/2 and z = 3/4. Discuss the complication that may arise when analytically continuing to the point z = 2.