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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2005 • Question 9

Question

Math 6210 • Real Analysis 2005 • Question 9

The series \[ f(z)=\sum _{n=1}^{\infty }\frac {1}{n^2}z^n \] defines a holomorphic function near the origin. Describe a maximal open subset of the complex plane on which \(f\) can be analytically continued.

Raw LaTeX

The series
\[
f(z)=\sum_{n=1}^{\infty}\frac{1}{n^2}z^n
\]
defines a holomorphic function near the origin. Describe a maximal open subset
of the complex plane on which \(f\) can be analytically continued.

Topic Tags

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