2018 Volume 61 Issue 1 Pages 109-133
We give a simple form of the evolution equation and a scalar Lax pair for the q-Garnier system. Some reductions to the q-Painlevé equations and the autonomous case as a generalized QRT system are discussed. Using two kinds of Padé problems on differential grid and q-grid, we derive some special solutions of the q-Garnier system in terms of the q-Appell Lauricella function and the generalized q-hypergeometric function.