Complete solution of the electrostatic equilibrium problem for classical weights

摘要

In this paper we complete the solution of the electrostatic equilibrium problem for all classical weight functions. In particular we solve this problem for classical generalized Bessel, Jacobi on (0, +∞) and pseudo-Jacobi weights. In addition we present an elementary unified way of dealing with the electrostatic equilibrium problem, which depends on the weights satisfying the Pearson differential equation.