Definition:Continued Product/Propositional Function/Iverson's Convention

Definition

Let $\ds \prod_{\map R j} a_j$ be the continued product over all $a_j$ such that $j$ satisfies $R$.

This can also be expressed:

$\ds \prod_{j \mathop \in \Z} a_j^{\sqbrk {\map R j} }$

where $\sqbrk {\map R j}$ is Iverson's convention.

Multiplicand

The set of elements $\set {a_j \in S}$ is called the multiplicand.

Notation

The sign $\ds \prod$ is called the product sign and is derived from the capital Greek letter $\Pi$, which is $\mathrm P$, the first letter of product.

Also see

• Results about continued products can be found here.

Historical Note

The originally investigation into the theory of infinite products was carried out by Leonhard Paul Euler.