Asymptotic properties of Helne-Stieltjes and van Vleck polynomials

Authors:
A. Martinez-Finkelshtein;E. B. Saff
Affiliations:
Departmento de Estadistí/ca y Mathemá/tica Aplicada, University of Almerí/a, Almerí/a, Spain/ and Instituto Carlos I de Fí/sica Teó/rica y Computacional, Granada University ...;Department of Mathematics, Vanderbilt University, Nashville, Tennessee
Venue:
Journal of Approximation Theory
Year:
2002

Citing 2
Cited 3

Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions

Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Variations on a theme of Heine and Stieltjes: an electrostatic interpretation of the zeros of certain polynomials

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Electrostatic models for zeros of polynomials: Old, new, and some open problems

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Choquet order for spectra of higher Lamé operators and orthogonal polynomials

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On a class of equilibrium problems in the real axis

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Abstract

We study the asymptotic behavior of the zeros of polynomial solutions of a class of generalized Lamé differential equations, when their coefficients satisfy certain asymptotic conditions. The limit distribution is described by an equilibrium measure in the presence of an external field, generated by charges at the singular points of the equation. Moreover, a case of non-positive charges is considered, which leads to an equilibrium with a non-convex external field.