The function $\dfrac{z}{\sin\pi z^{2}}$ of complex variable $z$. It has a simple pole at $z=0$. There is also 4 poles at $z=\pm\sqrt{n}$ and $z=\pm i\sqrt{n}$ (Where $n\in Z^{+}$). I need to find the order of the pole.please help me on this.
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1Does this answer your question? Singularities of $f(z)=\dfrac{z}{\sin\pi z^{2}}$? – Rodrigo de Azevedo May 12 '22 at 15:05
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All zeros of $\sin$ are of order 1 and located at $\pi\Bbb Z$.
The order of the zero $z=0$ of $\sin z^2$ is 2 because $z^2$ has a zero of order 2 at 0 (and $\sin$ has a simple zero there).
Hence, all poles of $z/\sin z$ are of order 1.
emacs drives me nuts
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