ON THE ITERATED POLYNOMIAL REGULARISATION OF THE DIFFERENTIAL SYSTEM RELATED TO THE GENERALISED MEIXNER ORTHOGONAL POLYNOMIALS

In this paper, we study the iterated polynomial regularisation of the differential system related to the generalised Meixner orthogonal polynomials. We show how recurrence coefficients of these polynomials are related to the fifth Painlevé equation by using a sequence of resolutions of indeterminacy points of the initial differential system. We also examine how the final charts differential systems after the first iteration are related by Bäcklund transformations of the fifth Painlevé equation.