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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2015 • Question 8

Question

Math 6210 • Real Analysis Fall 2015 • Question 8

Does there exist \(f:\mathbb D\to \mathbb C\) holomorphic so that \[ f\left (\frac {1}{n}\right )f\left (\frac {1}{n+1}\right )=\frac {1}{n} \] for all \(n\in \{2,3,\ldots \}\)?

Raw LaTeX

Does there exist \(f:\mathbb D\to\mathbb C\) holomorphic so that
\[
f\left(\frac{1}{n}\right)f\left(\frac{1}{n+1}\right)=\frac{1}{n}
\]
for all \(n\in\{2,3,\ldots\}\)?

Topic Tags

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