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We give a simple form of the evolution equation and a scalar Lax pair for the$q$-Garnier system. Some reductions to the $q$-Painlev\'e equations and theautonomous case as a generalized QRT system are discussed. Using two kinds ofPad\'e problems on differential grid and $q$-grid, we derive some specialsolutions of the $q$-Garnier system in terms of the $q$-Appell Lauricellafunction and the generalized $q$-hypergeometric function.

Study of $q$-Garnier system by Pad\'e method