“product notation”的概念、定义、翻译、参考文献-科学参考

product notation

Mathematics

单词	product notation
释义	product notation Mathematics For a finite sequence a₁, a₂,…, a_n, the product a₁ a₂…a_n may be denoted, using the capital Greek letter pi, by $\prod_{r = 1}^{n} a_{r} .$ where r is a dummy variable. For example, $\prod_{r = 1}^{9} (1 - \frac{1}{r + 1}) = (1 - \frac{1}{2}) (1 - \frac{1}{3}) \dots (1 - \frac{1}{10}) .$ Similarly, from an infinite sequence a₁, a₂, a₃,…, an infinite product a₁a₂a₃…can be formed, and it is denoted by $\prod_{r = 1}^{\infty} a_{r} .$ This notation is also used for the limit of the infinite product, if it exists. For example $\prod_{r = 2}^{\infty} (1 - \frac{1}{r^{2}}) = \frac{1}{2} .$ and also as in Wallis’ product.
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