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# Residue Laurent Series Help watch

1. Can anyone help me out with this question please?

Find the residue of:

f(z)=1/(e^(z)-1) at z=0

I can't seem to expand this through a Laurent expansion. Has anyone got a simple solution to working it out step by step please.
2. (Original post by coheed94)
Can anyone help me out with this question please?

Find the residue of:

f(z)=1/(e^(z)-1) at z=0

I can't seem to expand this through a Laurent expansion. Has anyone got a simple solution to working it out step by step please.
Until somebody more experienced comes by:

, now let , so we get:

I'll let you do the simplification.

You should get
Spoiler:
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and hopefully Greg/atsruser/firegarden/somebody will correct me if I'm wrong.
3. (Original post by Zacken)
Until somebody more experienced comes by:

, now let , so we get:

I'll let you do the simplification.

You should get
Spoiler:
Show
and hopefully Greg/atsruser/firegarden/somebody will correct me if I'm wrong.
(Original post by coheed94)
Can anyone help me out with this question please?

Find the residue of:

f(z)=1/(e^(z)-1) at z=0

I can't seem to expand this through a Laurent expansion. Has anyone got a simple solution to working it out step by step please.
too late ...
I would do the same
4. (Original post by Zacken)
and hopefully Greg/atsruser/firegarden/somebody will correct me if I'm wrong.
Looks right to me. Getting at residues often involves hacking at it with the mathematical equivalent of a machete.
5. (Original post by Gregorius)
Looks right to me. Getting at residues often involves hacking at it with the mathematical equivalent of a machete.
Thanks. They have their occasional elegance once in a blue moon.
6. (Original post by Gregorius)
Looks right to me. Getting at residues often involves hacking at it with the mathematical equivalent of a machete.
Can't we pierce it with a rapier by saying that since:

then has a pole of order 1 at 0, so that limit also gives the residue?

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