Asymptotic properties of Heine--Stieltjes and Van Vleck polynomials.

DOI10.1006/jath.2002.3705zbMath1099.33502OpenAlexW1991711762MaRDI QIDQ1867510

Edward B. Saff, Andrei Martínez-Finkelshtein

Publication date: 2 April 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.2002.3705

zbMATH Keywords

electrostaticslogarithmic potentialequilibrium distributionzero asymptoticsVan Vleck polynomialsgeneralized Lamé differential equationHeine--Stieltjes polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (17)

Electrostatic models for zeros of polynomials: old, new, and some open problems ⋮ On a class of equilibrium problems in the real axis ⋮ Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight ⋮ Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials ⋮ Choquet order for spectra of higher Lamé operators and orthogonal polynomials ⋮ Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials ⋮ On spectral polynomials of the Heun equation. II ⋮ Pair correlation statistics for the zeros of Lamé polynomials ⋮ A generalization of the Heine-Stieltjes theorem ⋮ On higher Heine-Stieltjes polynomials ⋮ Central limit theorems for the zeros of Lamé polynomials ⋮ How to find a measure from its potential ⋮ Equilibrium measures in the presence of certain rational external fields ⋮ On external fields created by fixed charges ⋮ On the distribution and interlacing of the zeros of Stieltjes polynomials ⋮ Phase transitions and equilibrium measures in random matrix models ⋮ Integrability-preserving regularizations of Laplacian Growth

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• Lamé differential equations and electrostatics
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