(adsbygoogle = window.adsbygoogle || []).push({}); Reimann sums, okay. How about a "Reimann product"?

An integral is a sort of "continuous sum". Very roughly, the sumΣgoes over to the integral_{k}f(x_{k}) Δx∫f(x)dxwhen the number of terms becomes infinite whileΔxgoes to zero.

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

Π_{k}[f(x_{k})]^{ Pk}

and let the exponentsPgo to zero while the number of products goes to infinite (and the range of_{k}xis 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 iseraised to an integral withln(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?

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# Reimann sums, okay. How about a Reimann product ?

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