Infinite product
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.
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Infinite product
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.
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En mathématiques, étant donnée ...... d vers l'infini ; notation : .
@fr
En oändlig produkt är inom mat ...... , kan en sådan produkt skrivas
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Iloczyn nieskończony – pojęcie ...... zeczywistych lub zespolonych).
@pl
In de wiskunde wordt voor een ...... John Wallis (Wallis-product):
@nl
In matematica si dice prodotto ...... o se converge la serie dei pn.
@it
In mathematics, for a sequence ...... John Wallis (Wallis product):
@en
Nekonečný součin je pojem mate ...... í konvergence nekonečných řad.
@cs
В математике для последователь ...... нию сходимости числового ряда.
@ru
У математиці, для послідовност ...... огічних результатам для рядів.
@uk
في الرياضيات، بالنسبة للمتتالي ...... عشر وهما على التوالي كما يلي:
@ar
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En mathématiques, étant donnée ...... d vers l'infini ; notation : .
@fr
En oändlig produkt är inom mat ...... , kan en sådan produkt skrivas
@sv
Iloczyn nieskończony – pojęcie ...... zeczywistych lub zespolonych).
@pl
In de wiskunde wordt voor een ...... oneindige product convergeert.
@nl
In matematica si dice prodotto ...... genza per i prodotti infiniti.
@it
In mathematics, for a sequence ...... nverse is in general not true.
@en
Nekonečný součin je pojem mate ...... inován pro všechna an a platí:
@cs
В математике для последователь ...... нию сходимости числового ряда.
@ru
У математиці, для послідовност ...... огічних результатам для рядів.
@uk
في الرياضيات، بالنسبة للمتتالي ...... عشر وهما على التوالي كما يلي:
@ar
label
Iloczyn nieskończony
@pl
Infinite product
@en
Nekonečný součin
@cs
Oneindig product
@nl
Oändlig produkt
@sv
Prodotto infinito
@it
Produit infini
@fr
Unendliches Produkt
@de
Бесконечное произведение
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Нескінченний добуток
@uk