The class one principal series Whittaker functions W_{n,a}(z) are central to the Fourier development of automorphic forms on GL(n,R). Of particular interest are the Mellin transforms M_{n,a}(s) of W_{n,a}(z). Until recently, explicit formulas for M_{n,a}(s) had been deduced only for n <= 4. In this talk, I will discuss joint work with Eric Stade that gives an explicit formula for M_{5,a}(s) as a double integral of Barnes type. Further, we use identities among hypergeometric series of type _4F_3(1) to show that, for special values of s, this Mellin transform reduces to a ratio of gamma functions.
This talk should be accessible to all.