# Can there be a symbol for continuous product?

We know that continuous version of $\sum$ is $\int$, but, can there be a continuous version of $\Pi$?

• Equally loosely speaking, $\,\prod = e^{\sum \ln }\,$. – dxiv Jul 10 '17 at 6:07
• $e^{\int \log}?$ ${}$ – Chris Jul 10 '17 at 6:07
• – Rahul Jul 10 '17 at 6:17
• @dxiv That works if we product integrate a positive (or at least nonnegative) function, but the product integral is more interesting for operators (e.g. matrices) that don't commute. – md2perpe Jul 10 '17 at 7:36

## 1 Answer

There is indeed: it is called the product integral.

• Hah, my off-the-cuff idea actually means something. Also, wow. (+1) – Chris Jul 10 '17 at 6:10
• I guess there won't be any for exponentiation or tetration, right? – ankit Jul 10 '17 at 6:27
• @ankit I'm not aware of continuous analogs for these. – user1337 Jul 10 '17 at 6:29
• @ankit I don't suppose you can define any continuum-limit if the underlying operation is not associative. – leftaroundabout Jul 10 '17 at 16:09