Complete solution of the electrostatic equilibrium problem for classical weights

DOI10.1016/j.amc.2011.11.084zbMath1243.78011OpenAlexW2003452159MaRDI QIDQ434627

Ryszard Smarzewski, Przemysław Rutka

Publication date: 16 July 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.11.084

zbMATH Keywords

classical orthogonal polynomialsSturm-Liouville differential equationPearson differential equationelectrostatic equilibrium problemweighted discriminants

Mathematics Subject Classification ID

Related Items (5)

Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials ⋮ Explicit barycentric formulae for osculatory interpolation at roots of classical orthogonal polynomials ⋮ Difference inequalities and barycentric identities for classical discrete iterated weights ⋮ The Szegö-Markov-Bernstein inequalities and barycentric representations of the osculatory interpolating operators for classical iterated weights ⋮ The electrostatic equilibrium problem for classical discrete orthogonal polynomials

Uses Software

• retode

Cites Work

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• An electrostatics model for zeros of general orthogonal polynomials
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• Electrostatic models for zeros of polynomials: old, new, and some open problems
• On Pólya frequency functions. I. The totally positive functions and their Laplace transforms
• Interpolation Processes
• Inequalities of Chernoff type for finite and infinite sequences of classical orthogonal polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Classical orthogonal polynomials with weight function ((ax + b)² + (cx + d)²)^−pexp(qArctg((ax + b)/(cx + d))),x ∈ (−∞, ∞) and a generalization of T and F distributions
• On the solution of some distributional differential equations: existence and characterizations of the classical moment functionals
• ON A CHARACTERIZATION OF MEIXNER'S POLYNOMIALS
• A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it
• Another Characterization of the Classical Orthogonal Polynomials
• A New Class of Orthogonal Polynomials: The Bessel Polynomials
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