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Proceedings of the American Mathematical Society

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

 

 

Pole- and zero-free regions for analytic continued fractions


Author: Hans-J. Runckel
Journal: Proc. Amer. Math. Soc. 97 (1986), 114-120
MSC: Primary 30C15; Secondary 30B70, 33A40
DOI: https://doi.org/10.1090/S0002-9939-1986-0831398-0
MathSciNet review: 831398
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Abstract: By using well-known methods of analytic continued fraction theory, various types of zero-free regions are obtained for sequences of polynomials having complex coefficients and being defined by three-term recurrence relations. These results are related to recent investigations by P. Henrici, E. B. Saff and R. S. Varga. As an application, zero-free sectors and stripes in $ {\mathbf{C}}$ are obtained for the Bessel function $ {J_v}$, where $ v$ is complex. Analogous results are obtained for the Lommel polynomials associated with $ {J_v}$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0831398-0
Article copyright: © Copyright 1986 American Mathematical Society