A linear second-order ODE with only polynomial solutions

DOI10.1016/J.JDE.2013.06.007zbMath1288.34002OpenAlexW1983085845MaRDI QIDQ2434671

Francesco Calogero

Publication date: 6 February 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2013.06.007

zbMATH Keywords

ODEs with polynomial solutionssecond-order ODEs with only polynomial solutionssolvable second-order ODEs

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Linear ordinary differential equations and systems (34A30)

Related Items (4)

On linear equations with general polynomial solutions ⋮ On the Zeros of Polynomials Satisfying Certain Linear Second-Order ODEs Featuring Many Free Parameters ⋮ 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 ⋮ Rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials

Cites Work

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• Can thegeneralsolution of the second-order ODE characterizing Jacobi polynomials bepolynomial?
• Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials
• Novel solvable variants of the goldfish many-body model
• Goldfishing: A new solvable many-body problem
• A solvable many-body problem, its equilibria, and a second-order ordinary differential equation whose general solution is polynomial

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