- #1

pellman

- 684

- 5

**Reimann sums, okay. How about a "Reimann product"?**

An integral is a sort of "continuous sum". Very roughly, the sum

*Σ*goes over to the integral

_{k}f(x_{k}) Δx*∫f(x)dx*when the number of terms becomes infinite while

*Δx*goes to zero.

What about a similar "continuous product"? If we have the product

Π

_{k}

*[f(x*

_{k})]^{ Pk}and let the exponents

*P*go to zero while the number of products goes to infinite (and the range of

_{k}*x*is fixed as in an integral) what sort of an animal do we get?

_{k}I realize that we can turn this product into a sum by taking the anti-logarithm. Then the continuous limit of this product is

*e*raised to an integral with

*ln(f)*in the integrand. However, I'm curious if the properties of these sorts of entities are known without resorting to integrals. And is there a notation for them?