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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

1999 • Question 7

Question

Math 6210 • Real Analysis 1999 • Question 7

Let \(\lambda >1\). Use Rouche’s Theorem to show that the equation \(\lambda -z-e^{-z}=0\) has one solution for \(\operatorname {Re}(z)>0\).

Raw LaTeX

Let \(\lambda>1\). Use Rouche's Theorem to show that the equation
\(\lambda-z-e^{-z}=0\) has one solution for \(\operatorname{Re}(z)>0\).

Topic Tags

Argument Principle and Rouche's Theorem