Equilibrium of charges and differential equations solved by polynomials. (English) Zbl 1108.34004
Summary: We study limits of particular importance of the bilinear hypergeometric equation. As part of this study, we examine connections between the rationality of certain indefinite integrals and the equilibrium of Coulomb charges in the complex plane (or point vortices in two-dimensional hydrodynamics). Relationships with integrable models which are generalizations of the Calogero-Moser systems are also discussed.
MSC:
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 33C52 | Orthogonal polynomials and functions associated with root systems |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 78A35 | Motion of charged particles |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
