Formulae are derived for the characteristic function of the inverted Dirichlet distribution and hence the multivariate F . The analysis involves a new function with multiple arguments that extends the confluent hypergeometric function of the second kind. This function and its properties are studied in the paper and a simple integral representation is given which is useful for numerical work. A special case connected with the multivariate t distribution is also explored.
Phillips, Peter C.B., "Distributions" (1988). Cowles Foundation Discussion Papers. 1108.