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Laurent Series $\sum_{n=-1}^\infty a_n x^n$ when $a_{-1} = \infty$

When dealing with complex functions, if $f(x)$ has a simple pole, then we can find the coefficient $a_{-1}$ in the Laurent expansion $f(x) = \sum_{n=-1}^\infty a_n x^n$ by evaluating the limit $\lim_{...
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