  It is proved that the mean signature of multi-dimensional fractional brownian
motion admits a meromorphic continuation in the hurst parameter to the entire
complex plane. Each contstituent mean iterated integral is a sum of
hypergeometric integrals indexed by the pair partitions which refine the
partition arising from the sequential list of integrands which defines it.
Furthermore, each such hypergeometric integral is holomorphic in the complement
of a finite union of rational progressions determined by the combinatorial
structure of the pair partition which defines it. It is not proved that these
singularities actually exist, it is only proved that the singularities are of
finite order and they can only occur in the specified discrete set of rational
numbers.
