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    Hi, could anyone help me to work out the laurent series of

    (sinz)/z^4 around z=0 please!

    I have no idea where to start!

    thanks
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    (Original post by drbunhead)
    Hi, could anyone help me to work out the laurent series of

    (sinz)/z^4 around z=0 please!

    I have no idea where to start!

    thanks
    what techniques do you know for finding laurent series?

    Do you know a series for sin z that might help you?
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    (Original post by davros)
    what techniques do you know for finding laurent series?

    Do you know a series for sin z that might help you?
    Hi, I used the Taylor expansion for sin z, and then divided by z^4
    Which gives the series for |z|<0 but how do you find out |z|>0 ?

    Thank you!
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    (Original post by drbunhead)
    Hi, I used the Taylor expansion for sin z, and then divided by z^4
    Which gives the series for |z|<0 but how do you find out |z|>0 ?

    Thank you!
    There's no such thing as |z|<0. |z|>=0 for all complex numbers z.

    The only time you have different Laurent series is when you have different regions of convergence.
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    (Original post by davros)
    There's no such thing as |z|<0. |z|>=0 for all complex numbers z.

    The only time you have different Laurent series is when you have different regions of convergence.
    Oh okay! Makes more sense now!
    So what if the isolated singularity z=0 is inside a unit circle?
    Do we have to work out |z| <1 ?

    For |z| > 1 would the series be 0 ?

    Thanks
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    (Original post by drbunhead)
    Oh okay! Makes more sense now!
    So what if the isolated singularity z=0 is inside a unit circle?
    Do we have to work out |z| <1 ?

    For |z| > 1 would the series be 0 ?

    Thanks
    It depends on the series! In this case, |z|=1 has no special significance - you should know that the Taylor/Maclaurin series for sin z converges everywhere, so the only issue with (sin z)/z^4 is at the point z = 0 itself.
 
 
 
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