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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2021 • Question 2

Question

Math 6220 • Complex Analysis Fall 2021 • Question 2

Without quoting Picard’s theorems, show that if \(f\) is entire and not a polynomial then for every \(\epsilon >0\) there exists \(p\in \mathbb {C}\) so that \(|f(p)-p^2|<\epsilon \).

Raw LaTeX

Without quoting Picard's theorems, show that if \(f\) is entire and not a polynomial
then for every \(\epsilon>0\) there exists \(p\in\mathbb{C}\) so that \(|f(p)-p^2|<\epsilon\).

Topic Tags

Entire Functions and Liouville-Type Theorems Picard-Type Theorems and Casorati-Weierstrass