Hurwitz,s Root Theorem
المؤلف:
Krantz, S. G
المصدر:
"Hurwitz,s Theorem." §5.3.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser
الجزء والصفحة:
...
22-7-2021
3005
Hurwitz's Root Theorem
Let ![<span style=]()
{f_n(x)}" src="https://mathworld.wolfram.com/images/equations/HurwitzsRootTheorem/Inline1.gif" style="height:15px; width:40px" /> 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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