A whittaker function of matrix argument

Whittaker functions arise naturally in many topics in physical, biological, and social sciences, such as input-output situations in econometric problems, storage-consumption situations, growth-decay situations, when dealing with bilinear forms in random variables, and so on. An account of some of these is available in Mathai (1993). The matrix-variate analogue is considered in this article. A Whittaker function of matrix argument is defined, and several new results on this function are established in this paper, complementing the results given earlier by Mathai and Pederzoli (1996). Some of these generalize the corresponding results in the scalar variable case.