An alternative derivation of closed-form representations for multidimensional lattice sums of generalized hypergeometric functions

Some representations for infinite m-dimensional lattice sums of generalized hypergeometric functions, which were deduced previously by the first-named author, are rederived here by appealing to an alternative more direct meth od. In particular, it is shown that these lattice sums are proportional to a finite sum of Meijer's G-functions.