The product integral is the multiplicative version of standard integrals. Indefinite products are the discrete counterpart to this integral; they multiply iterations on a function $f(x)$ by each other.
Is there a simple relation between the two? If so, what is this relation?
Motivation
This may give an alternative (although fairly roundabout) to calculating summations. It can be seen in the indefinite product link above that the indefinite product is related to summations by a fairly simple relation. If there exists another fairly simple relation between product integrals and indefinite products, this would provide an alternative to summations, via product integrals.
Secondly, I'm interested in exploring indefinite products, and this may provide an easy alternative.