Equations of motion for zeros of orthogonal polynomials related to the Toda lattices

DOI10.1016/j.ajmsc.2010.06.001zbMath1216.33024OpenAlexW2147813250MaRDI QIDQ531701

Wen-Xiu Ma, Mourad E. H. Ismail

Publication date: 19 April 2011

Published in: Arab Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ajmsc.2010.06.001

zbMATH Keywords

partition functiondiscriminantszeros of orthogonal polynomialsmotions of zeros

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items (5)

On a Direct Uvarov-Chihara Problem and Some Extensions ⋮ On polynomials associated with an Uvarov modification of a quartic potential Freud-like weight ⋮ Orthogonal polynomials and perturbations on measures supported on the real line and on the unit circle. A matrix perspective ⋮ Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis ⋮ Nonisospectral extension of Schur flow with determinant solution and orthogonal polynomials on the unit circle

Cites Work

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• Theory of nonlinear lattices.
• Discriminants and functions of the second kind of orthogonal polynomials
• Tau-function constructions of the recurrence coefficients of orthogonal polynomials
• An electrostatics model for zeros of general orthogonal polynomials
• Rational solutions of the Toda lattice equation in Casoratian form
• Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials
• Ladder operators and differential equations for orthogonal polynomials
• Generalized Casorati Determinant and Positon–Negaton-Type Solutions of the Toda Lattice Equation

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