IIT JAM Follow
August 10, 2020 7:16 am 80 pts
1. Let S = {z E C: |z| < 2} and let T denotes the boundary of S. Find interior points, exterior points, boundary points and accumulation points of T. Does there exists a sequence (z7) in T such that the series n=1 converges? Justify your answer. Expand the function 1/(2- z) into the Maclaurin series valid in the diskS. If f: S >T is a function such that f is analytic everywhere in S, prove that f is constant throughout S. If g: C > T is an entire function, prove that g is constant throughout the complex plane.
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