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Date: 29-5-2021
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Date: 5-6-2021
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Let be a sequence of analytic functions regular in a region , and let this sequence be uniformly convergent in every closed 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:
Krantz, S. G. "Hurwitz's Theorem." §5.3.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 76, 1999.
Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 22, 1975.
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