In complex analysis, functions are studied that are differentiable (in the complex space) at almost all points. Zeroes and poles are very important concept.

Zeros are termed as points at which a function .

A Pole (also called an isolated singularity) is a point where the limit of a complex function inflates dramatically with polynomial growth.

More specifically, a point is a pole of a complex valued function f if the function value tends to infinity as gets closer to . If the limit is finite, then is not a pole.

is a pole of order if:

What is done here is is multiplied by and then taking limit as approaches . If the result is not equal to , then is a pole.

Order of Zeros