Zero-free parabolic regions for polynomials with complex coefficients

Runckel, Hans-J.

doi:10.1090/S0002-9939-1983-0695262-X

Zero-free parabolic regions for polynomials with complex coefficients
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by Hans-J. Runckel PDF

Proc. Amer. Math. Soc. 88 (1983), 299-304 Request permission

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 $\delta$.

References

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