Confluent hypergeometric function of second kind with matrix argument (Q1086398)

In this paper, we have generalized confluent hypergeometric function of second kind to the matrix argument. Its connections with certain other special functions defined by Herz, some of its differential properties, and an interesting confluence have also been established. In the last section, we have applied our theory in the field of multivariate statistical analysis by finding the distribution of Bartlett's criterion: \[ V_ 1=\frac{(\det A_ 1)^{{1/2}n_ 1}(\det A_ 2)^{{1/2}n_ 2}}{\det (A_ 1+A_ 2)^{1/2}(n_ 1+n_2)} \] for testing the hypothesis: \(H_ 1=\Sigma_ 1=\Sigma_ 2\).