Answered: Problem 10.3 4 Show that the following…

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

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)

Expert Solution

Step 1

Let us consider the function $f (z) = u + i v$ .

To show the function is entire.

$\frac{\partial u}{\partial x}, \frac{\partial u}{\partial y}, \frac{\partial v}{\partial x}, \frac{\partial v}{\partial y}$ is continuous.
$\begin{array}{rcl} \frac{\partial u}{\partial x} & = & \frac{\partial v}{\partial y}, \frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x} \end{array}$ .

The Sum of the entire functions is entire.

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