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mathematical analysis > calculus > sequence > infinite product

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infinite product

In mathematics, for a sequence of complex numbers a₁, a₂, a₃, ... the infinite product

${\\displaystyle \\prod _{n=1}^{\\infty }a_{n}=a_{1}a_{2}a_{3}\\cdots }$

is defined to be the limit of the partial products a₁a₂...a_n 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 a_n as n increases without bound must be 1, while the converse is in general not true.

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Infinite_product)

sequence

produit infini

français

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http://data.loterre.fr/ark:/67375/PSR-K39D3VZK-8

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RDF/XML TURTLE JSON-LD Date de création 21/08/2023, dernière modification le 21/08/2023