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Complex Analysis / Singularities : Now, prove that a function f has an essential singularity at z = a iff neither of the above holds for any real number s.

One can classify isolated singularities by examining the equations:

lim (z -> a) |z - a|^s |f(z)| = 0

lim(z -> a) |z - a|^s |f(z)| = infinity

Now, prove that a function f has an essential singularity at z = a iff neither of the above holds for any real number s.

Solution Summary

Singularites are investigated. The solution is detailed and well presented.

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