Pole- and zero-free regions for analytic continued fractions
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- by Hans-J. Runckel PDF
- Proc. Amer. Math. Soc. 97 (1986), 114-120 Request permission
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 ${J_v}$.References
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- Hans-J. Runckel, Zero-free parabolic regions for polynomials with complex coefficients, Proc. Amer. Math. Soc. 88 (1983), no. 2, 299–304. MR 695262, DOI 10.1090/S0002-9939-1983-0695262-X
- E. B. Saff and R. S. Varga, Zero-free parabolic regions for sequences of polynomials, SIAM J. Math. Anal. 7 (1976), no. 3, 344–357. MR 414968, DOI 10.1137/0507028
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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