Hurwitz's Root Theorem
Let 
be a Sequence of Analytic Functions Regularin a region 
, and let this sequence be Uniformly Convergent in everyClosed Subset of . If the Analytic Function
does not vanish identically, then if
is a zero of 
of order 
, a Neighborhood 
of and a number 
exist such that if 
, 
has exactly zeros in .
References
Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 22, 1975.
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