“Hurwitz's Root Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Hurwitz's Root Theorem

释义

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

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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