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On the sharpness of theorems concerning zero-free regions for certain sequences of polynomials

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Summary

In this paper, we establish the sharpness of a theorem concerning zero-free parabolic regions for certain sequences of polynomials satisfying a three-term recurrence relation. Similarly, we establish the sharpness of a zero-free sectorial region for certain sequences of Padé approximants toe z.

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Authors and Affiliations

  1. Dept. of Mathematics, University of South Florida, 33620, Tampa, Florida, U.S.A.

    E. B. Saff

  2. Dept. of Mathematics, Kent State University, 44242, Kent, Ohio, U.S.A.

    R. S. Varga

Authors
  1. E. B. Saff
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  2. R. S. Varga
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Additional information

Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2688

Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2729, and by the Energy Research and Development Administration (ERDA) under Grant E(11-1)-2075

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Saff, E.B., Varga, R.S. On the sharpness of theorems concerning zero-free regions for certain sequences of polynomials. Numer. Math. 26, 345–354 (1976). https://doi.org/10.1007/BF01409957

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  • DOI: https://doi.org/10.1007/BF01409957

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