Limit of the "productory"

Question

With the term "productory" I just mean $\Pi_{i=m}^nx_i$ but I do not know the english term. My question is:
is there a limit for such an expression in the same sense as the limit of a sum is an integral, i.e. $\lim_{\delta x\rightarrow 0}\Sigma y(x)\delta x = \int y(x) dx$?
Has it any application?

score 3 · Accepted Answer · edited Apr 13 '17 at 12:19

3

Yes, there is!

It is called product integral. I think it was introduced by Vito Volterra for probability applications. A standard reference about it is: "Product Integration with Applications to Differential Equations", by Dollard and Friedman.

Also, check out this question here.

edited Apr 13 '17 at 12:19

Community

1

answered Jun 03 '14 at 16:25

geodude

8,065

Limit of the "productory"

1 Answers1