See also
Argument Principle
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References
Challener, D. and Rubel, L. "A Converse to Rouché's Theorem." Amer. Math. Monthly 89, 302-305, 1982.Estermann,
T. Complex
Numbers and Functions. London: Oxford University Press, p. 156, 1962.Knopp,
K. Theory
of Functions Parts I and II, Two Volumes Bound as One, Part II. New York:
Dover, p. 111, 1996.Krantz, S. G. "Rouché's Theorem."
§5.3.1 in Handbook
of Complex Variables. Boston, MA: Birkhäuser, p. 74, 1999.Szegö,
G. Orthogonal
Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 22, 1975.Referenced
on Wolfram|Alpha
Rouché's Theorem
Cite this as:
Weisstein, Eric W. "Rouché's Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RouchesTheorem.html
Subject classifications
and 
analytic in 
with 
a simple loop homotopic to
a point in 
,
if 
for all 
on 
,
then 
and 
have the same number of roots inside 
.
