Unformatted text preview: every neighborhood of z Non-Isolated Singularities Singularities for which f ( z ) is not analytic in a deleted neighborhood of z . Branch Points: The point z is a branch point of f ( z ) if there is a discontinuity in f ( z ) after a small circuit around z . Non-isolated Essential Singularities: The point z is a non-isolated essential singularity of f ( z ) if isolated singularities of f ( z ) cluster around z so that there is no deleted neighborhood of z in which f ( z ) is analytic. Note: Examine singularities at the point at inﬁnity by making the substitution f (1 /w ) and exam-ining w → ....
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- Fall '09
- Z0, Pole, singularity, singularities, Isolated Essential Singularities