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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2021 • Question 8

Question

Math 6220 • Complex Analysis Fall 2021 • Question 8

Give an example of a domain \(D\) and a holomorphic function \(f:D\to \mathbb {C}\), so that \(f\) is not given by a single Laurent series on \(D\). (Please include a proof.)

Raw LaTeX

Give an example of a domain \(D\) and a holomorphic function \(f:D\to\mathbb{C}\), so that
\(f\) is not given by a single Laurent series on \(D\). (Please include a proof.)

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Laurent Series and Annuli Zeros of Holomorphic Functions and the Identity Theorem