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

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 the 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 the ladder operator approach, we obtain a pair of second-order nonlinear difference equations and a pair of differential–difference equations satisfied by the recurrence coefficients αn(s) and βn(s). We also …