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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