Rational Function
Laurent expansion
If
is single-valued in 
, then
Isolated singular point
If
is single-valued regular in 
but not regular in 
, then 
is an isolated singular point.
- Removable singular point
- Pole of order
- Essential singular point
Residue
Residue principle
If
is single-valued regular except on points 
inside 
and also on any simple closed curve 
inside 
, then
Argument principle
If
is rational inside 
, and also regular and non-zero on a simple closed curve 
inside 
, then the following is true, where 
is the number of zeros and 
is the number of poles of 
inside 
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