I am having some confusion about Laurent series at infinity and essential singularities. Consider the function: $$f(z)=\frac{1}{1-z}$$ which has a Laurent Series about infinity of: $$f(z)=-\frac{1}{z}-\frac{1}{z^2}-...$$ From this it would appear that $f(z)$ would have an essential singularity. However, $$f(t)=\frac{t}{t-1}$$ Where $t=1/z$ does not have an essential singularity at $t=0$ which would mean that $f(z)$ does not have an essential singularity at $z=\infty$. Which of my reasonings is right and why is the other wrong?
2026-03-29 06:04:38.1774764278
Laurent series about infinity and essential singularities?
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