The Recurrence Coefficients of Orthogonal Polynomials with a Weight Interpolating between the Laguerre Weight and the Exponential Cubic Weight

In this paper, we consider the orthogonal polynomials with respect to weight w(x)=w(x;s):=xλe−N[x+s(x3−x)],x∈R+, where λ>0, N>0 and 0≤s≤1. By using ladder operator approach, obtain a pair of second-order nonlinear difference equations differential–difference satisfied by recurrence coefficients αn(s) βn(s). We also establish relation between associated Hankel determinant coefficients. From Dyson’s Coulomb fluid prove that converge limits are derived explicitly when q:=n/N is fixed as n→∞.