Continuous products

jostpuur
Rough idea behind integration is to sum lot's of small numbers (close to zero). Some problems lead to situations where you have to multiply lot's of numbers close to one. Is there any general theory of such products? Important results or tools?

Eighty
The first is called a series or an infinite sum. The second is called an infinite product.

$$\prod_{k=0}^n \exp(iH_k \Delta t /\hbar)$$, where product cannot be turned into sum in the exponent always since $$H_k$$ do not always commute.