On differential systems related to generalized Meixner and deformed Laguerre orthogonal polynomials

In this paper we present a connection between systems of differential equations for the recurrence coefficients polynomials orthogonal with respect to generalized Meixner and deformed Laguerre weights. It is well-known that both can be expressed in terms solutions fifth Painlevé equation but no explicit relation was known. We also certain limits which XXXIV equation, case extends previous studies new result.