无穷乘积

在数学中，对于复数串行 a₁, a₂, a₃, ...，无穷乘积

\prod_{n=1}^{\infty} a_n = a_1 \; a_2 \; a_3 \cdots

定义为部分乘积a₁a₂...a_n在n的增加没有边界时的极限。当这个极限存在并且不是0的时候，这个乘积称为“收敛”，否则称为发散。

单词	Infinite product
释义	Infinite product 中文百科无穷乘积在数学中，对于复数串行 a₁, a₂, a₃, ...，无穷乘积 $\prod_{n=1}^{\infty} a_n = a_1 \; a_2 \; a_3 \cdots$ 定义为部分乘积a₁a₂...a_n在n的增加没有边界时的极限。当这个极限存在并且不是0的时候，这个乘积称为“收敛”，否则称为发散。英语百科 Infinite product 无穷乘积 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...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.
随便看	Siebenmann antrum irrigating cannula的意思 Siebenmanncanal的意思 siebenmann canals的意思 Siebenmann maxillary artrum cannula的意思 Siebenmann spiral ended cotton carrier的意思 Sieber的意思 Sieber crocus的意思 Sieber number的意思 siebers的意思 Siebert的意思 Siebert furnace的意思 siebes的意思 Siebold的意思 Siebold and Bradbury test的意思 Siebold and Bradbury test letter的意思 siebold buttercup herb的意思 siebold clubmoss herb的意思 Siebold deutzia的意思 Siebold Euphorbia Root的意思 siebold greenbrier rhizome and root的意思 Siebold Greenbrier Root and Rhizome的意思 Sieboldiana的意思 sieboldii的意思 sieboldius deflexus的意思 siebold knotweed fruit or herb的意思

Infinite product

无穷乘积

Infinite product 无穷乘积