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An isolated singularity at which the Laurent expansion has infinitely many negative powers is called

  • A.a pole of finite order
  • B.removable
  • C.essential
  • D.a simple pole

Answer: C

A removable singularity has no negative powers, a pole of order \( m \) has finitely many down to \( (z - z_{0})^{-m} \), and an essential singularity has infinitely many. The standard example is \( e^{1/z} \) at the origin, near which the function takes every value infinitely often, so no limit exists in any sense

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