Pole- and zero-free regions for analytic continued fractions

Runckel, Hans-J.

doi:10.1090/S0002-9939-1986-0831398-0

Pole- and zero-free regions for analytic continued fractions
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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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