If z = a is an isolated singularity of f and \(f\left( z \right) = \mathop \sum \limits_{ - \infty }^\infty {a_n}{\left( {z - a} \right)^n}\) is its Laurent expansion in ann (a; 0, R), then z = a is a removable singularity if

1
an = 0, n ≤ -1
2
an ≠ 0, n ≤ -1
3
an = 0, n ≥ -1
4
an ≠ 0, n ≥ -1

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