  The Lauricella theory of multiple hypergeometric functions is used to shed
some light on certain distributional properties of the mean of a Dirichlet
process. This approach leads to several results, which are illustrated here.
Among these are a new and more direct procedure for determining the exact form
of the distribution of the mean, a correspondence between the distribution of
the mean and the parameter of a Dirichlet process, a characterization of the
family of Cauchy distributions as the set of the fixed points of this
correspondence, and an extension of the Markov-Krein identity. Moreover, an
expression of the characteristic function of the mean of a Dirichlet process is
obtained by resorting to an integral representation of a confluent form of the
fourth Lauricella function. This expression is then employed to prove that the
distribution of the mean of a Dirichlet process is symmetric if and only if the
parameter of the process is symmetric, and to provide a new expression of the
moment generating function of the variance of a
  Dirichlet process.
