Gibbs Partitions (EPPF's) Derived From a Stable Subordinator are Fox H and Meijer G Transforms

Understand

This paper derives explicit results for the infinite Gibbs partitions generated by the jumps of an $\alpha-$stable subordinator, derived in Pitman \cite{Pit02, Pit06}.

• We first show that for general $\alpha$ the conditional EPPF can be represented as ratios of Fox-$H$ functions, and in the case of rational $\alpha,$ Meijer-G functions.
• Furthermore the results show that the resulting unconditional EPPF's, can be expressed in terms of H and G transforms indexed by a function h.
• Hence when h is itself a H or G function the EPPF is also an H or G function.