Electrostatic interpretation for the zeros of certain polynomials and the Darboux process

DOI10.1016/S0377-0427(00)00661-0zbMath0989.42006MaRDI QIDQ5946612

F. Alberto Gruenbaum

Publication date: 9 July 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

zeros of polynomialsDarboux processelectrostatic interpretationStieltjesthree term recurrence relation

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Real polynomials: location of zeros (26C10) Electro- and magnetostatics (78A30)

Related Items (10)

The Darboux process and a noncommutative bispectral problem: some explorations and challenges ⋮ Electrostatic models for zeros of polynomials: old, new, and some open problems ⋮ Incenter of triangle as a stationary point ⋮ Stable equilibria for the roots of the symmetric continuous Hahn and Wilson polynomials ⋮ On a class of equilibrium problems in the real axis ⋮ Zeros of orthogonal polynomials generated by canonical perturbations of measures ⋮ On equilibrium concyclic configurations ⋮ Finite Blaschke products with prescribed critical points, Stieltjes polynomials, and moment problems ⋮ Orthogonal polynomial solutions of linear ordinary differential equations ⋮ Electrostatic interpretation of zeros of orthogonal polynomials

Cites Work

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• Some functions that generalize the Krall-Laguerre polynomials
• An electrostatics model for zeros of general orthogonal polynomials
• The impact of Stieltjes' work on continued fractions and orthogonal polynomials: Additional material
• General methods for constructing bispectral operators
• Ladder operators and differential equations for orthogonal polynomials
• Lamé differential equations and electrostatics

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