(a) Consider the function f (z) Ln(1 z). What is the radius of the largest circle
Chapter 19, Problem 32(choose chapter or problem)
(a) Consider the function \(f(z)=\operatorname{Ln}(1+z)). What is the radius of the largest circle centered at the origin within which f is analytic?
(b) Expand f in a Maclaurin series. What is the radius of convergence of this series?
(c) Use the result in part (b) to find a Maclaurin series for \(\operatorname{Ln}(1-z)).
(d) Find a Maclaurin series for \(\operatorname{Ln}\left(\frac{1+z}{1-z}\right)\).
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