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## Homework Statement

Hi all.

According to my book, a pole [itex]z_0[/itex] of a function f(z) is defined as

[tex]

\mathop {\lim }\limits_{z \to z_0 } f(z) = \infty.

[/tex]

Now lets look at e.g. f(z) = exp(z). Thus we have a singularity for z = infinity, since the limit in this case is infinity.

This is what I don't understand: Definitions aside, f(z) = exp(z) is still analytic when it is infinite, so how can there be a singularity there?