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On the Location of the Zeros of a Polynomial

✍ Scribed by R.B. Gardner; N.K. Govil

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
134 KB
Volume
78
Category
Article
ISSN
0021-9045

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✦ Synopsis

The classical EnestΓΆm-Kekeya Theorem states that a polynomial (p(z)=) (\sum_{i=0}^{n} a_{i} z^{\prime}) satisfying (0<a_{0} \leq a_{1} \leq \cdots \leq a_{n}) has all its zeros in (|z| \leq 1). We extend this result to a larger class of polynomials by dropping the conditions that the coefficients be real and positive and weakening the hypothesis that coefficients be monotonic increasing. Our result generalizes and sharpens several known results. 1994 Academic Press, Inc.

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