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of a [[sequence]] of numbers ''a''<sub>1</sub>, ''a''<sub>2</sub>, ''a''<sub>3</sub>, ... is defined to be the [[limit (mathematics)|limit]] of the partial products ''a''<sub>1</sub>''a''<sub>2</sub>...''a''<sub>''n''</sub> as ''n'' goes to infinity. The infinite product is said to [[convergence|converge]] when the limit exists and is not zero. Otherwise the product is said to [[diverge]].
of a [[sequence]] of numbers ''a''<sub>1</sub>, ''a''<sub>2</sub>, ''a''<sub>3</sub>, ... is defined to be the [[limit (mathematics)|limit]] of the partial products ''a''<sub>1</sub>''a''<sub>2</sub>...''a''<sub>''n''</sub> as ''n'' goes to infinity. The infinite product is said to [[convergence|converge]] when the limit exists and is not zero. Otherwise the product is said to [[diverge]].
==Infinite Product representations of entire functions==
==Infinite Product representation of entire functions==
[[Karl Weierstrass]] proved that every [[entire function]] ''f''(''z'') with a divergent sequence (λ<sub>''n''</sub>) of zeros, can be factored into an infinite product of the form
[[Karl Weierstrass]] proved that every [[entire function]] ''f''(''z'') with a divergent sequence (λ<sub>''n''</sub>) of zeros, can be factored into an infinite product of the form
:<math>
:<math>
[[category:mathematics]]
[[category:mathematics]]
[[category:complex analysis]]