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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

1999 • Question 9

Question

Math 6210 • Real Analysis 1999 • Question 9

Let \(f\) be an injective entire function. Put \(g(z)=f(1/z)\). Show that \(g\) does not have an essential singularity at \(0\). In particular, it follows that \(f(z)=az+b\). Why?

Raw LaTeX

Let \(f\) be an injective entire function. Put \(g(z)=f(1/z)\). Show
that \(g\) does not have an essential singularity at \(0\). In particular, it
follows that \(f(z)=az+b\). Why?

Topic Tags

Automorphism Groups and Biholomorphisms Entire Functions and Liouville-Type Theorems Isolated Singularities and Residues