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An electrostatics model for zeros of general orthogonal polynomials. (English) Zbl 1011.33011
The author extends the Stieltjes models from Jacobi orthogonal polynomials to general orthogonal polynomials satisfying integrability conditions on their weight functions. It was proved that the zeros of general orthogonal polynomials determine the equilibrium position of movable n unit charges in an external field determined by the weight function. The total energy of the system was computed in terms of the recursion coefficients of the orthogonal polynomials. The limiting behavior as the number of particles tending to infinity was studied in the case of Freud exponential weights.

MSC:
33C45Orthogonal polynomials and functions of hypergeometric type
78A30Electro- and magnetostatics