Category:Infinite Products

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This category contains results about Infinite Products.
Definitions specific to this category can be found in Definitions/Infinite Products.


Let an infinite number of values of $j$ satisfy the propositional function $R \left({j}\right)$.

Then the precise meaning of $\displaystyle \prod_{R \left({j}\right)} a_j$ is:

$\displaystyle \prod_{R \left({j}\right)} a_j = \left({\lim_{n \mathop \to \infty} \prod_{\substack {R \left({j}\right) \\ -n \mathop \le j \mathop < 0} } a_j}\right) \times \left({\lim_{n \mathop \to \infty} \prod_{\substack {R \left({j}\right) \\ 0 \mathop \le j \mathop \le n} } a_j}\right)$

provided that both limits exist.

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

Pages in category "Infinite Products"

The following 47 pages are in this category, out of 47 total.