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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2024 • Question 2

Question

Math 6220 • Complex Analysis Fall 2024 • Question 2

Let \(f:B(0,1)\to \mathbb {C}\) be holomorphic. Describe all such \(f\) that satisfy \[ f\left (\frac {1}{n}\right )=\frac {n^2-2n-1}{n^2} \] for every \(n\in \{2,3,\ldots \}\).

Raw LaTeX

Let \(f:B(0,1)\to\mathbb{C}\) be holomorphic. Describe all such \(f\) that satisfy
\[
f\left(\frac{1}{n}\right)=\frac{n^2-2n-1}{n^2}
\]
for every \(n\in\{2,3,\ldots\}\).

Topic Tags

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