Definition: Products

A product is an expression of the form $a_1\cdot a_2\cdot\ldots\cdot a_n$ for a finite number of elements. This can be also written more shortly using the $\prod$ symbol:

$$\prod_{i=1}^n a_i.$$

If there are infinitely many number of elements we want to multiply, we write more generally $$\prod_{i\in I} a_i,$$ where $I$ is an arbitrary index set.

Proofs: 1
Propositions: 2

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  1. Miller, Kenneth S.: "An Introduction to the Calculus of Finite Differences And Difference Equations", Dover Publications, Inc, 1960