Definition:Convergent Product

Also defined as
Some authors do not require the limit to be nonzero for the product to converge. The phrase:
 * $\displaystyle \prod_{n \mathop = 1}^\infty a_n$ diverges to $0$

then becomes:
 * $\displaystyle \prod_{n \mathop = 1}^\infty a_n$ converges to $0$.

This flexibility is common when dealing with uniform convergence.

Also see

 * Value of Convergent Infinite Product is Well-Defined
 * Definition:Absolute Convergence of Product