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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2017 • Question 9

Question

Math 6420 • PDE Spring 2017 • Question 9

Prove that if all singularities of an analytic function \(f(z)\) in the extended complex plane \(\overline {\mathbb {C}}\) are poles, then \(f(z)\) is a rational function (i.e. the ratio of two polynomials).

Raw LaTeX

Prove that if all singularities of an analytic function \(f(z)\) in the extended complex
plane \(\overline{\mathbb{C}}\) are poles, then \(f(z)\) is a rational function
(\textit{i.e.} the ratio of two polynomials).

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Isolated Singularities and Residues Linear Programming and Optimization Meromorphic Functions and the Argument Principle