Calculus of principal series Whittaker functions on SL(n,R)SL(n,R)

We study Whittaker functions for the principal series representations of SL(n,R)SL(n,R). We derive a system of partial differential equations characterizing our Whittaker functions. We give explicitly power series solutions at the regular singularity of the system, and integral representations of the unique moderate growth Whittaker functions.