Journal of Physics A, Mathematical and Theoretical vol:44 issue:3 pages:035202
We consider a semi-classical version of the Meixner weight depending on two parameters and the associated set of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the coefficients appearing in this relation satisfy a discrete Painlevé equation, which is a limiting case of an asymmetric dPIV equation. Moreover, when viewed as functions of one of the parameters, they satisfy one of Chazy’s second-degree
Painlevé equations, which can be reduced to the fifth Painlevé equation PV.