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A Laurent expansion differs from a Taylor expansion in that it also carries

  • A.fractional powers of the displacement from the centre
  • B.a finite number of terms only
  • C.logarithmic terms alongside the powers
  • D.negative powers of the displacement from the centre

Answer: D

A Laurent series runs over all integer powers, \( \sum_{n=-\infty}^{\infty} a_{n}(z-z_{0})^{n} \), and converges in an annulus rather than a disc. The negative powers are what let it represent a function round an isolated singularity, and the coefficient \( a_{-1} \) is the residue there

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