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 finite_product_of_complex_numbers [2014/03/21 11:11]127.0.0.1 external edit finite_product_of_complex_numbers [2015/04/28 14:34]nikolaj Both sides previous revision Previous revision 2015/04/28 14:35 nikolaj 2015/04/28 14:34 nikolaj 2015/04/17 21:41 nikolaj 2014/03/21 11:11 external edit2013/09/09 15:55 nikolaj 2013/09/08 16:05 nikolaj 2013/09/08 15:48 nikolaj 2013/09/07 19:43 nikolaj 2013/09/07 19:37 nikolaj 2013/09/07 19:36 nikolaj created Next revision Previous revision 2015/04/28 14:35 nikolaj 2015/04/28 14:34 nikolaj 2015/04/17 21:41 nikolaj 2014/03/21 11:11 external edit2013/09/09 15:55 nikolaj 2013/09/08 16:05 nikolaj 2013/09/08 15:48 nikolaj 2013/09/07 19:43 nikolaj 2013/09/07 19:37 nikolaj 2013/09/07 19:36 nikolaj created Last revision Both sides next revision Line 1: Line 1: ===== Finite product of complex numbers ===== ===== Finite product of complex numbers ===== - ==== Set ==== + ==== Function ​==== - | @#55CCEE: context ​    | @#55CCEE: $(z_i) \in \mathrm{FinSequence}(\mathbb C)$ | + | @#FF9944: definition  ​| @#FF9944: it $\equiv$ Finite sum over a monoid w.r.t $\langle\!\langle ​{\mathbb C},\cdot \rangle\!\rangle$ | - | @#55CCEE: context ​    | @#55CCEE: $n = \mathrm{length}((z_i)) ​$ | + - | @#FFBB00: definiendum | @#FFBB00: $\prod: \mathrm{FinSequence}(\mathbb C)\to \mathbb C$ | + ----- - | @#FFBB00: definiendum | @#​FFBB00: ​$\prod_{i=1}^n\ z_i:= \begin{cases} ​1 & \mathrm{if}\ n=0\\\\ ​\left(\prod_{i=1}^{n-1}\ z_i\right)\ \cdot\ z_n & \mathrm{else} \end{cases}$ | + $2\prod_{k=2}^{n-1}\left(1+\frac{1}{k}\right)=n$ - + ----- - ==== Discussion ==== + - ==== Parents ==== + === Subset of === === Subset of === [[Finite sum over a monoid]] [[Finite sum over a monoid]] + === Requirements === + [[Complex number]]