On the zeros of generalized Bessel polynomials. II

Bruin, Marcel G. de; Saff, Edward B.; Varga, Richard S.

doi:10.1016/1385-7258(81)90014-7

Cited by 14 publications

(15 citation statements)

References 10 publications

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“…We remark that a special case of (2.10) of Theorem 3 was previously established in de Bruin et al [5]. Specifically, for the case σ = 1 and n j odd for all j ≥ 1 of (2.3), it was shown in [5, eq.…”

Section: Corollary 2 If Under the Hypothesis Of (23) Of Theorem 1mentioning

confidence: 91%

Asymptotics for the zeros and poles of normalized Pad\'{e} approximants to ${\rm e}^{z}$

Varga

Carpenter

1994

Numerische Mathematik

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With s n (z) denoting the n-th partial sum of e z , the exact rate of convergence of the zeros of the normalized partial sums, s n (nz), to the Szegő curve D 0,∞ was recently studied by Carpenter et al. (1991), where D 0,∞ is defined by D 0,∞ := {z ∈ C : |ze 1−z | = 1 and |z| ≤ 1}.Here, the above results are generalized to the convergence of the zeros and poles of certain sequences of normalized Padé approximants R n,ν ((n + ν)z) to e z , where R n,ν (z) is the associated Padé rational approximation to e z .

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Section: Corollary 2 If Under the Hypothesis Of (23) Of Theorem 1mentioning

confidence: 91%

Asymptotics for the zeros and poles of normalized Pad\'{e} approximants to ${\rm e}^{z}$

Varga

Carpenter

1994

Numerische Mathematik

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“…Stated in terms of generalized Bessel polynomials (1.11)-(1.12) asymptotic results on zeros are due to De Bruin et al [4], Carpenter [5], and Wong and Zhang [31]. These papers deal with the limit (1.13) with A = 2.…”

Section: Earlier Work On Asymptoticsmentioning

confidence: 99%

Riemann-Hilbert Analysis for Laguerre Polynomials with Large Negative Parameter

Kuijlaars

McLaughlin

2001

Comput. Methods Funct. Theory

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Abstract. We study the asymptotic behavior of Laguerre polynomials L (αn) n (nz) as n → ∞, where α n is a sequence of negative parameters such that −α n /n tends to a limit A > 1 as n → ∞. These polynomials satisfy a non-hermitian orthogonality on certain contours in the complex plane. This fact allows the formulation of a Riemann-Hilbert problem whose solution is given in terms of these Laguerre polynomials. The asymptotic analysis of the Riemann-Hilbert problem is carried out by the steepest descent method of Deift and Zhou, in the same spirit as done by Deift et al. for the case of orthogonal polynomials on the real line. A main feature of the present paper is the choice of the correct contour.

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“…If z,(7) denotes the number of zeros z of O,((2n+a-2)z/2;a) which satisfy arg z~ <arg z<arg z2, then de Bruin et al [4] showed that lim z. (7)_ ~2-~bl n-*c~ n This result implies that, for n large and any fixed a~R, the zeros of 0.…”

Section: The Dr ~ Curvementioning

confidence: 89%