PlanetMath: $z_0$ is a pole of $f$

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is a pole of $f$

(Definition)

Let be an analytic function on a punctured neighborhood of $x_0\in\mathbf{C}$ , that is, analytic on

$\displaystyle \{z\in C: 0<\vert z-x_0\vert<\varepsilon\}$

for some $\varepsilon>0$ and such that

$\displaystyle \lim_{z \rightarrow z_0} \vert f(z)\vert = \infty.$

We say then that

is a pole for

is a pole of $f$

" is owned by drini. [ full author list (3) | owner history (2) ]

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Cross-references: pole, neighborhood, analytic function
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This is version 4 of $z_0$

, born on 2003-10-15, modified 2005-02-26.
Object id is 4919, canonical name is Z_0IsAPoleOfF.
Accessed 1539 times total.

Classification:

30A99 (Functions of a complex variable :: General properties :: Miscellaneous)

Pending Errata and Addenda

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