Category:Definitions/Infinite Products

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This category contains definitions related to Infinite Products.
Related results can be found in Category:Infinite Products.


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

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

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

provided that both limits exist.

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

Subcategories

This category has only the following subcategory.

Pages in category "Definitions/Infinite Products"

The following 39 pages are in this category, out of 39 total.