Confluent KZ equations for sl_N with Poincare rank 2 at infinity

We construct confluent KZ equations with Poincare rank 2 at infinity for the case of sl_N and the integral representation for the solutions. Hamiltonians of these confluent KZ equations are derived from suitable quantization of dlog tau constructed in the theory of monodromy preserving deformation by Jimbo, Miwa and Ueno. Our confluent KZ equations may be viewed as a quantization of monodromy preserving deformation with Poincare rank 2 at infinity.