Definition:Oscillating Product

Definition

An infinite product which is neither convergent nor divergent is known as an oscillating product.

Examples

Arbitrary Example

The infinite product:

$\ds \prod \paren {-1}^n$

is an oscillating product, as it oscillates between the values $+1$ and $-1$.

Also see

• Definition:Divergent Product
• Definition:Convergent Product

• Results about oscillating products can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): infinite product
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): infinite product