Symbols:Greek/Pi/Product Notation
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Continued Product
- $\ds \prod_{j \mathop = 1}^n a_j$
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 continued product of $\tuple {a_1, a_2, \ldots, a_n}$, and is written:
- $\ds \prod_{j \mathop = 1}^n a_j = \paren {a_1 \times a_2 \times \cdots \times a_n}$
The $\LaTeX$ code for \(\ds \prod_{j \mathop = 1}^n a_j\) is \ds \prod_{j \mathop = 1}^n a_j
.
The $\LaTeX$ code for \(\ds \prod_{1 \mathop \le j \mathop \le n} a_j\) is \ds \prod_{1 \mathop \le j \mathop \le n} a_j
.
The $\LaTeX$ code for \(\ds \prod_{\map \Phi j} a_j\) is \ds \prod_{\map \Phi j} a_j
.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols