Argument Principle
المؤلف:
Duren, P.; Hengartner, W.; and Laugessen, R. S
المصدر:
"The Argument Principle for Harmonic Functions." Amer. Math. Monthly 103
الجزء والصفحة:
...
17-11-2018
970
Argument Principle
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
REFERENCES:
Duren, P.; Hengartner, W.; and Laugessen, R. S. "The Argument Principle for Harmonic Functions." Amer. Math. Monthly 103, 411-415, 1996.
Knopp, K. Theory of Functions, Parts I and II. New York: Dover, pp. 132-134, 1996.
Krantz, S. G. "The Argument Principle." Ch. 5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 69-78, 1999.
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