A Complex function has a pole of order at if, in the Laurent Series, for and . Equivalently, has a pole of order at if is the smallest Positive Integer for which is differentiable at . If , there is no pole at . Otherwise, the order of the pole is the greatest Positive Coefficient in the Laurent Series.

This is equivalent to finding the smallest such that

is differentiable at 0.

**References**

Arfken, G. *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 396-397, 1985.

© 1996-9

1999-05-25