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Thread: Poles of an exponential function

  1. #1
    Forum Admin topsquark's Avatar
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    Poles of an exponential function

    This is a bit embarrassing since I know I've done this problem before.

    I was trying to respond to a post and this problem came up. Where are the poles in the expression e^{-z^2}= cos(z^2) - i ~ sin(z^2)? I know it's a simple problem but I just can't wrap my mind about it.

    Thanks!

    -Dan
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Poles of an exponential function

    Quote Originally Posted by topsquark View Post
    Where are the poles in the expression e^{-z^2}= cos(z^2) - i ~ sin(z^2)? I know it's a simple problem but I just can't wrap my mind about it.
    There are no poles, f(z)=e^{-z^2} is holomorphic in \mathbb{C}.
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    Forum Admin topsquark's Avatar
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    Re: Poles of an exponential function

    Quote Originally Posted by FernandoRevilla View Post
    There are no poles, f(z)=e^{-z^2} is holomorphic in \mathbb{C}.
    Thanks. That was my first thought but I managed to make things complicated. It drives my students nuts because I will do a derivation in 10 lines that can often be done in two.

    -Dan
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