Construction of a Lax Pair for the [...] [...]-Painleve System

We construct a Lax pair for the [...] [...]-Painlevé system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices - the [...]-linear lattice - through a natural generalisation of the big [...]-Jacobi weight. As a by-product of our construction we derive the coupled first-order [...]-difference equations for the [...] [...]-Painlevé system, thus verifying our identification. Finally we establish the correspondences of our result with the Lax pairs given earlier and separately by Sakai and Yamada, through explicit transformations. [ProQuest: [...] denotes formulae omitted.]