On expressible sets of products

For a sequence of real numbers {a(n)}(n=1)infinity we call E-Pi{a(n)}(n=1)infinity = {Pi(infinity)(n=1) (1+1/a(n)c(n)) : c(n) is an element of Z(+)} its Pi-expressible set. In this paper we calculate E-Pi{a(n)}(n=1)(infinity) under various hypotheses on {a(n)}(n=1)(infinity). Where this is not possible we give partial information on its contents. In many ways, this analysis is a continuation of related investigations on the Sigma-expressible sets of sums.