On Toda lattices and orthogonal polynomials

DOI10.1016/S0377-0427(00)00673-7zbMath0989.42007MaRDI QIDQ5946623

Franz Peherstorfer

Publication date: 9 July 2002

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

zbMATH Keywords

elliptic functionsToda latticesPadé approximants of square-root functionsperiodic latticesperiodic recurrence coefficientspolynomials orthogonal on several intervals

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Classical equilibrium statistical mechanics (general) (82B05)

Related Items

Recurrence relations for the moments of discrete semiclassical orthogonal polynomials ⋮ A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials ⋮ Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations ⋮ Toda chain, Stieltjes function, and orthogonal polynomials ⋮ The symmetrization problem for multiple orthogonal polynomials ⋮ Moment modification, multipeakons, and nonisospectral generalizations ⋮ Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants ⋮ Comparative asymptotics for discrete semiclassical orthogonal polynomials ⋮ Nonlinear functional equations satisfied by orthogonal polynomials ⋮ Orthogonal functions related to Lax pairs in Lie algebras ⋮ Orthogonal polynomial interpretation of \(q\)-Toda and \(q\)-Volterra equations ⋮ Extended mixed function method and its application for solving two classic Toda lattice equations ⋮ Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs ⋮ Characterizations of \(\Delta\)-Volterra lattice: a symmetric orthogonal polynomials interpretation ⋮ Matrix Toda and Volterra lattices ⋮ Elliptic solutions of the Toda chain and a generalization of the Stieltjes-Carlitz polynomials ⋮ The matrix Toda equations for coefficients of a matrix three-term recurrence relation ⋮ Poisson brackets of orthogonal polynomials ⋮ On the Darboux transform and the solutions of some integrable systems ⋮ Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis ⋮ Extended relativistic Toda lattice, L-orthogonal polynomials and associated Lax pair

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