  The diagrammatic cumulant expansion for the periodic Anderson model with
infinite Coulomb repulsion ($U=\infty $) is considered here for an hypercubic
lattice of infinite dimension ($d=\infty $). The same type of simplifications
obtained by Metzner for the cumulant expansion of the Hubbard model in the
limit of $d=\infty $, are shown to be also valid for the periodic Anderson
model.
