Pole
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 Integerfor 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.See also Laurent Series, Residue (Complex Analysis)
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 396-397, 1985.
- Skew Quadrilateral
- Skew Symmetric Matrix
- Sklar's Theorem
- Skolem-Mahler-Lerch Theorem
- Skolem Paradox
- Skolem Sequence
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