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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.

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    When you say product integral, it seems you are referring to what Wikipedia calls the "geometric product integral". Is that correct?2018-03-18
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    It's been awhile, but I was interested in that, as well as "Type I", found in Wikipedia here: https://en.wikipedia.org/wiki/Product_integral#Type_I. I'll try to give this some more thought. I did find some ways of relating products found in the book "Non-Newtonian Calculus" by Grossman & Katz.2018-03-19

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