## POLE

### Pole

In the mathematical field of complex analysis, a pole of a meromorphic function is a certain type of singularity that behaves like the singularity of $\frac{1}{z^n}$ at z = 0. For a pole of the function f at point a the function approaches infinity as z approaches a.

The above text is a snippet from Wikipedia: Pole (complex analysis)

### pole

#### Noun

1. Originally, a stick; now specifically, a long and slender piece of metal or (especially) wood, used for various construction or support purposes.
2. A type of basic fishing rod.
3. A long fiberglass sports implement used for pole-vaulting.
4. A telescope used to identify birds, aeroplanes or wildlife.
5. A unit of length, equal to a perchchain or 5½ yards).
6. Pole position.

#### Noun (etymology 2)

1. Either of the two points on the earth's surface around which it rotates; also, similar points on any other rotating object.
2. A point of magnetic focus, especially each of the two opposing such points of a magnet (designated north and south).
3. A fixed point relative to other points or lines.
4. A contact on an electrical device (such as a battery) at which electric current enters or leaves.
5. For a meromorphic function $f(z)$: a point $a$ for which $f(z) \rightarrow \infty$ as $z \rightarrow a$.
The function $f(z) = \frac{1}{z-3}$ has a single pole at $z = 3$.
6. The firmament; the sky.

#### Verb

1. To propel by pushing with poles, to push with a pole.
Huck Finn poled that raft southward down the Mississippi because going northward against the current was too much work.
2. To identify something quite precisely using a telescope.
He poled off the serial of the Gulfstream to confirm its identity.
3. To furnish with poles for support.
to pole beans or hops
4. To convey on poles.
to pole hay into a barn
5. To stir, as molten glass, with a pole.

#### Verb (etymology 2)

1. To induce piezoelectricity in (a substance) by aligning the dipoles.

The above text is a snippet from Wiktionary: pole