If is meromorphic in a region enclosed by a contour , let be the number of complex roots of in , and be the number of poles in , with each zero and pole counted as many times as its multiplicity and order, respectively. Then
Defining and gives
If is meromorphic in a region enclosed by a contour , let be the number of complex roots of in , and be the number of poles in , with each zero and pole counted as many times as its multiplicity and order, respectively. Then
Defining and gives
Weisstein, Eric W. "Argument Principle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ArgumentPrinciple.html