In mathematics, for a sequence of complex numbers a1, a2, a3, ... the infinite product
is defined to be the limit of the partial products a1a2...an as n increases without bound. The product is said to converge when the limit exists and is not zero. Otherwise the product is said to diverge. A limit of zero is treated specially in order to obtain results analogous to those for infinite sums. Some sources allow convergence to 0 if there are only a finite number of zero factors and the product of the non-zero factors is non-zero, but for simplicity we will not allow that here. If the product converges, then the limit of the sequence an as n increases without bound must be 1, while the converse is in general not true.
The best known examples of infinite products are probably some of the formulae for π, such as the following two products, respectively by Viète and John Wallis (Wallis product):
Read more about Infinite Product: Convergence Criteria, Product Representations of Functions
Famous quotes containing the words infinite and/or product:
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (16231662)
“Good is a product of the ethical and spiritual artistry of individuals; it cannot be mass-produced.”
—Aldous Huxley (18941963)