Poles or Removable Singularities

[Chris0724]

Homework Statement

Determine the location and nature of singularities in the finite z plane of the follow function and apply Cauchy Integral Formula

Homework Equations

g(z) =

sin 2z
-------
z^15

The Attempt at a Solution

I know there is a pole of order 14 at z = o

but I'm a bit confuse when i apply the Cauchy Integral Formula

{sin 2z } / z
------------
```z^15

= 2 pi j { d ^13 f(z) / dz}
```````-----------------
`````````````13!

= 2 pi j / 13! <-- correct ?

many thanks! :)

 

[Dick]

You'd better take another careful look at the Cauchy integral theorem. I don't know where you got the '13' and what is that f(z) that you are taking the 13th derivative of? Why did it just disappear?

 

[Chris0724]

You'd better take another careful look at the Cauchy integral theorem. I don't know where you got the '13' and what is that f(z) that you are taking the 13th derivative of? Why did it just disappear?

hi,

i think i make a mistake...

sin 2z
-------
z^15

since sin 2z is analytic, f(z) = sin 2 z

2 pi j { d^14 f(z) / dz }

= 2 pi j { 0 }

= 0 <-- correct ?

 

[Dick]

hi,

i think i make a mistake...

sin 2z
-------
z^15

since sin 2z is analytic, f(z) = sin 2 z

2 pi j { d^14 f(z) / dz }

= 2 pi j { 0 }

= 0 <-- correct ?

That's better. You are missing a 1/14! But it doesn't matter because the derivative is zero anyway.