Zeros of exceptional orthogonal polynomials and the maximum of the modulus of an energy function

Abstract

We propose a new property of the zeros of exceptional orthogonal polynomials. It has been known that exceptional orthogonal polynomials (XOP) have both real and complex zeros. By fixing m variables at the imaginary parts of the complex zeros of XOP, we find that in some cases the modulus of the energy function of a many-particle system attains its maximum at the zeros of XOP. We give a sufficient condition for this result with respect to the denominators of the weight function of XOP.