Whittaker functions for generalized principal series representations of SL(3, R)

We study Whittaker functions for generalized principal series representations of the real special linear group SL(3, R) of degree 3. From the Capelli elements and Dirac-Schmid operators, we give the system of partial differential equations which is satisfied by Whittaker functions. We give six formal power series solutions of this system, which are called secondary Whittaker functions. We also give the Mellin-Barnes type integral expressions of primary Whittaker functions, i.e. the solutions having the moderate growth property.