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Problem 10.3 4 Show that the following function is entire. f(z)=cosh(z)

Problem 10.3 4 Show that the following function is entire. f(z)=cosh(z)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 10.3 4 Show that the following function is entire. f(z)=cosh(z)
Transcribed Image Text:Problem 10.3 4 Show that the following function is entire. f(z)=cosh(z)
Expert Solution
Step 1

Let us consider the function f(z)=u+iv.

To show the function is entire. 

  1. ∂u∂x,∂u∂y,∂v∂x,∂v∂y is continuous.
  2. ∂u∂x=∂v∂y, ∂u∂y=-∂v∂x.

The Sum of the entire functions is entire.

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