Show that if \(f:\{z:0<|z|<1\}\to \mathbb {C}\) is meromorphic and has poles at \(\frac {1}{2},\frac {1}{3},\frac {1}{4},\ldots \) then the range of \(f\) is dense in \(\mathbb {C}\).
Question
Math 6220 • Complex Analysis
Fall 2020 • Question 5
Question
Fall 2020 • Question 5
Show that if \(f:\{z:0<|z|<1\}\to \mathbb {C}\) is meromorphic and has poles at \(\frac {1}{2},\frac {1}{3},\frac {1}{4},\ldots \) then the range of \(f\) is dense in \(\mathbb {C}\).