Polynomials satisfying functional and differential equations and Diophantine properties of their zeros

DOI10.1007/S11005-013-0612-YzbMath1273.70019OpenAlexW2092755945MaRDI QIDQ353295

Francesco Calogero, Ge Yi

Publication date: 12 July 2013

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-013-0612-y

zbMATH Keywords

isochronous dynamical systemssolvable dynamical systemssolvable Newtonian many-body problemsclassical polynomialsDiophantine relations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) (n)-body problems (70F10) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Related Items (5)

Properties of the zeros of generalized basic hypergeometric polynomials ⋮ Properties of the zeros of the polynomials belonging to the Askey scheme ⋮ Properties of the zeros of the polynomials belonging to the \(q\)-Askey scheme ⋮ Diophantine Properties Associated to the Equilibrium Configurations of an Isochronous N-Body Problem ⋮ Equilibria of a solvable N-body problem and related properties of the N numbers x _n at which the Jacobi polynomial of order N has the same value

Cites Work

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• Another new solvable many-body model of goldfish type
• A new class of solvable many-body problems
• Can thegeneralsolution of the second-order ODE characterizing Jacobi polynomials bepolynomial?
• Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials
• Isochronous Systems

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