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A short proof of a continued fraction test for the stability of polynomials


Author: R. M. Hovstad
Journal: Proc. Amer. Math. Soc. 105 (1989), 76-79
MSC: Primary 30C15; Secondary 30B70
DOI: https://doi.org/10.1090/S0002-9939-1989-0973839-7
MathSciNet review: 973839
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Abstract: A generalized form related to the usual test fraction is used in an induction proof giving a quick access to the stability test for complex polynomials.


References [Enhancements On Off] (What's this?)

  • [1] W. B. Jones and W. J. Thron, Continued fractions, analytic theory and applications, Encyclopedia of Mathematics and Its Applications, Vol. 11, Addison-Wesley, Reading, Massachusetts, 1980. Distributed now by Cambridge Univ. Press. MR 595864 (82c:30001)
  • [2] H. S. Wall, Polynomials whose zeros have negative real parts, Amer. Math. Monthly 52 (1945), 308-322. MR 0012709 (7:62g)
  • [3] E. Frank, On the zeros of polynomials with complex coefficients, Bull. Amer. Math. Soc. 52 (1946), 144-157. MR 0014509 (7:295d)

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DOI: https://doi.org/10.1090/S0002-9939-1989-0973839-7
Article copyright: © Copyright 1989 American Mathematical Society

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