Definition:Continued Product/Propositional Function/Iverson's Convention
< Definition:Continued Product | Propositional Function(Redirected from Definition:Continued Product by Iverson's Convention)
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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.