An electrostatic model for zeros of classical Laguerre polynomials perturbed by a rational factor

n this paper, we study an electrostatic model for zeros of polynomials orthogonal with respect to inner product$$begin{aligned} leftlangle p,qrightrangle _{alpha ,eta }=int limits _{0}^{infty }p(x)q(x) frac{1}{x-eta },{rm d}mu (x), end{aligned}$$where ({rm d}mu (x)) is the classical Laguerre measure ({rm e}^{-x}x^{alpha },{rm d}x,) with (alpha -1) and (eta 0.)