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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Zero-free parabolic regions for polynomials with complex coefficients


Author: Hans-J. Runckel
Journal: Proc. Amer. Math. Soc. 88 (1983), 299-304
MSC: Primary 30C15; Secondary 30B70
DOI: https://doi.org/10.1090/S0002-9939-1983-0695262-X
MathSciNet review: 695262
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Abstract: Recent results by P. Henrici, E. B. Saff and R. S. Varga on zero-free parabolic regions for sequences of polynomials generated from three-term recurrence relations with real coefficients are generalized to complex coefficients by continued fraction methods. Especially, it is shown that all zeros of the generalized Bessel polynomials $ Y_n^{(\delta )}$ for complex $ \delta $ are contained in a cardioid region, which generalizes a result of E. B. Saff and R. S. Varga for real $ \delta $.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0695262-X
Article copyright: © Copyright 1983 American Mathematical Society