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analytic continuation

Source: miklos schweitzer 1996 q7

October 15, 2021
complex analysis

Problem Statement

Construct a holomorphic function f(z)=∑n=0∞anznf(z) = \sum \limits_{n = 0} ^ \infty a_n z^n ( | z | <1 ) in the unit circle that can be analytically continued to all points of the unit circle except one point, and for which the sequence {an}\{a_n\} has two limit points, ∞\infty and a finite value.
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