Lie Theory and the Lauricella Functions FD

It is shown that the Lauricella functions FD in n variables transform as basis vectors corresponding to irreducible representations of the Lie algebra sl(n+3,C). Group representation theory can then be applied to derive addition theorems, transformation formulas, and generating functions for the FD. It is clear from this analysis that the use of SL(m,C) symmetry in atomic and elementary particle physics will lead inevitably to the remarkable functions FD.