Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials

Denote by P̂n(α,β)(x) the X1X1-Jacobi polynomial of degree nn. These polynomials were introduced and studied recently by Gómez-Ullate, Kamran and Milson in a series of papers. In this note we establish some properties of the zeros of P̂n(α,β)(x), such as interlacing and monotonicity with respect to the parameters αα and ββ. They turn out to possess an electrostatic interpretation. The vector, whose components are the zeros, is a saddle point of the energy of the corresponding logarithmic field.