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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2016 • Question 6

Question

Math 6210 • Real Analysis Fall 2016 • Question 6

Let \(f(z)\) be an analytic function. Show that the successive derivatives of \(f(z)\) at a point can never satisfy \[ |f^{(n)}(z)|>n!n^n \] for all \(n\).

Raw LaTeX

Let \(f(z)\) be an analytic function. Show that the successive
derivatives of \(f(z)\) at a point can never satisfy
\[
|f^{(n)}(z)|>n!n^n
\]
for all \(n\).

Topic Tags

Analytic Continuation and Monodromy Holomorphic Functions and Cauchy-Riemann Equations