- #1
Winzer
- 598
- 0
Homework Statement
Determine the nature of the singularity at z=0
Homework Equations
[itex] f(z)=\frac{1}{cos(z)}+\frac{1}{z} [/itex]
The Attempt at a Solution
by expanding into series:
[itex] f(z)=\Sigma_{n=0}^{\infty} \frac{(2n)! (-1)^n}{x^{2n}} + \Sigma_{n=0}^{\infty} (-1)^n (z-1)^n[/itex]
Now [itex] \frac{1}{z}[/itex] has no principle part, [tex] b_m=0[/itex].
This leaves the only principle part from cos. [itex] b_m=(2m)! (-1)^m[/itex]. There are infinite bm
so the behaviour is an essential singularity.
I don't feel too confident about this answer. I feel I have overlooked a step.