Category:Examples of Infinite Products

From ProofWiki
Jump to navigation Jump to search

This category contains examples of Infinite Product.

Let an infinite number of values of $j$ satisfy the propositional function $\map R j$.

Then the precise meaning of $\displaystyle \prod_{\map R j} a_j$ is:

$\displaystyle \prod_{\map R j} a_j = \paren {\lim_{n \mathop \to \infty} \prod_{\substack {\map R j \\ -n \mathop \le j \mathop < 0} } a_j} \times \paren {\lim_{n \mathop \to \infty} \prod_{\substack {\map R j \\ 0 \mathop \le j \mathop \le n} } a_j}$

provided that both limits exist.

If either limit does fail to exist, then the infinite product does not exist.

Pages in category "Examples of Infinite Products"

This category contains only the following page.