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

Means of a Dirichlet process and multiple hypergeometric functions