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Math Help - Order of Poles of a Complex Function with Trigonometric Functions

  1. #1
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    Order of Poles of a Complex Function with Trigonometric Functions

    This really should be simple but it's not quite getting through my thick skull!!

    Given that the function 1/z^2 had a pole z_0=0 of order 2, does the function 1/(z^2 Sin[z]), with a particular pole at z_0=0, have order 2 or 3?
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  2. #2
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    Quote Originally Posted by Jippo
    This really should be simple but it's not quite getting through my thick skull!!

    Given that the function 1/z^2 had a pole z_0=0 of order 2, does the function 1/(z^2 Sin[z]), with a particular pole at z_0=0, have order 2 or 3?
    As \sin(z) \sim z near z=0 the pole is of order 3.

    RonL
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    Thanks very much Captain Black!
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