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Pole and residue

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    What are the poles and residues for 1/(exp(z)+1) ?

    Any help would be appreciated.

    (Original post by Vincent9231)

    What are the poles and residues for 1/(exp(z)+1) ?

    Any help would be appreciated.
    some more of your thoughts and input would help to see where you are getting stuck though.

    The numerator never vanishes.

    When does the denominator vanish? (hint: what values of z make the denominator vanish, think about the very famous equation by Euler).

    What about it's derivative does it vanish there?

    You can then use this to figure out the order of the pole at these singularities.

    Then use

    (Also L'Hopital's 0/0 will come in handy here unless you fancy working out the series)

    btw post to maths help not maths uni for a quicker reply.
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