# Symbols:Greek/Pi/Product Notation

## Product Notation

$\displaystyle \prod_{j \mathop = 1}^n a_j$

Let $\struct {S, \times}$ be an algebraic structure where the operation $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.

Let $\tuple {a_1, a_2, \ldots, a_n} \in S^n$ be an ordered $n$-tuple in $S$.

The composite is called the product of $\tuple {a_1, a_2, \ldots, a_n}$, and is written:

$\displaystyle \prod_{j \mathop = 1}^n a_j = \paren {a_1 \times a_2 \times \cdots \times a_n}$

The $\LaTeX$ code for $\displaystyle \prod_{j \mathop = 1}^n a_j$ is \displaystyle \prod_{j \mathop = 1}^n a_j .

The $\LaTeX$ code for $\displaystyle \prod_{1 \mathop \le j \mathop \le n} a_j$ is \displaystyle \prod_{1 \mathop \le j \mathop \le n} a_j .

The $\LaTeX$ code for $\displaystyle \prod_{\map \Phi j} a_j$ is \displaystyle \prod_{\map \Phi j} a_j .